106 (number)
106 (one hundred ndsix) is the natural number following 105 and preceding 107. In mathematics 106 is a centered pentagonal number, a centered heptagonal number A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by ..., and a regular 19-gonal number. There are 106 mathematical trees with ten vertices. See also * 106 (other) References {{DEFAULTSORT:106 (Number) Integers ...
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Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ...
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105 (number)
105 (one hundred ndfive) is the natural number following 104 and preceding 106. In mathematics 105 is a triangular number, a dodecagonal number, and the first Zeisel number. It is the first odd sphenic number and is the product of three consecutive prime numbers. 105 is the double factorial of 7. It is also the sum of the first five square pyramidal numbers. 105 comes in the middle of the prime quadruplet (101, 103, 107, 109). The only other such numbers less than a thousand are 9, 15, 195, and 825. 105 is also the middle of the only prime sextuplet (97, 101, 103, 107, 109, 113) between the ones occurring at 7-23 and at 16057–16073. As the product of the first three odd primes (3\times5\times7) and less than the square of the next prime (11) by > 8, for n=105, n ± 2, ± 4, and ± 8 must be prime, and n ± 6, ± 10, ± 12, and ± 14 must be composite (prime gap). 105 is also a pseudoprime to the prime bases 13, 29, 41, 43, 71, 83, and 97. The distinct prime factors of 105 a ...
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107 (number)
107 (one hundred ndseven) is the natural number following 106 and preceding 108. In mathematics 107 is the 28th prime number. The next prime is 109, with which it comprises a twin prime, making 107 a Chen prime. Plugged into the expression 2^p - 1, 107 yields 162259276829213363391578010288127, a Mersenne prime. 107 is itself a safe prime. It is the fourth Busy beaver number, the maximum number of steps that any Turing machine with 2 symbols and 4 states can make before eventually halting. It is the number of triangle-free graphs on 7 vertices. It is the ninth emirp, because reversing it's digits gives another prime number (701) In other fields As "one hundred ''and'' seven", it is the smallest positive integer requiring six syllables in English (without the "and" it only has five syllables and seventy-seven is a smaller 5-syllable number). 107 is also: * The atomic number of bohrium. * The emergency telephone number in Argentina and Cape Town. * The telephone of the poli ...
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Centered Pentagonal Number
A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for ''n'' is given by the formula :P_=, n\geq1 The first few centered pentagonal numbers are 1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391, 456, 526, 601, 681, 766, 856, 951, 1051, 1156, 1266, 1381, 1501, 1626, 1756, 1891, 2031, 2176, 2326, 2481, 2641, 2806, 2976 . Properties *The parity of centered pentagonal numbers follows the pattern odd-even-even-odd, and in base 10 the units follow the pattern 1-6-6-1. *Centered pentagonal numbers follow the following Recurrence relations: :P_=P_+5n , P_0=1 :P_=3(P_-P_)+P_ , P_0=1,P_1=6,P_2=16 *Centered pentagonal numbers can be expressed using Triangular Numbers: :P_=5T_+1 See also *Pentagonal number *Polygonal number *Centered polygonal number The centered polygonal numbers are a class of ...
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Centered Heptagonal Number
A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by the formula :\over2. The first few centered heptagonal numbers are 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953 Properties * Centered heptagonal numbers alternate parity in the pattern odd-even-even-odd. * A heptagonal numbers can expressed as a multiple of a triangular number by 7, plus one: :C_ = 7 * T_ + 1 *C_ is the sum of the integers between n+1 and 3n+1 (including) minus the sum of the integers from 0 to n (including). Centered heptagonal prime A centered heptagonal prime is a centered heptagonal number that is prime. The first few centered heptagonal primes are :43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, ... Due to parity, the centered heptagonal primes are in the form ...
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Tree (graph Theory)
In graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ..., a tree is an undirected graph in which any two Vertex (graph theory), vertices are connected by ''exactly one'' Path (graph theory), path, or equivalently a Connected graph, connected Cycle (graph theory), acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by ''at most one'' path, or equivalently an acyclic undirected graph, or equivalently a Disjoint union of graphs, disjoint union of trees. A polytreeSee . (or directed tree or oriented treeSee .See . or singly connected networkSee .) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirecte ...
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106 (other)
106 may refer to: *106 (number), the number *AD 106, a year in the 2nd century AD *106 BC, a year in the 2nd century BC *106 (emergency telephone number), an Australian emergency number *106 (MBTA bus), a route of the Massachusetts Bay Transportation Authority 10/6 may refer to: * October 6 (month-day date notation) * June 10 (day-month date notation) * 10 shillings and 6 pence in UK predecimal currency ** the value of the half guinea in predecimal shillings and pence ** ''10/6'', the price tag on the hat of the Hatter in ''Alice's Adventures in Wonderland'' See also * 1/6 (other), for uses of "1/06" *Seaborgium Seaborgium is a synthetic chemical element with the symbol Sg and atomic number 106. It is named after the American nuclear chemist Glenn T. Seaborg. As a synthetic element, it can be created in a laboratory but is not found in nature. It is als ...