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Search: id:A007781
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| 1, 3, 23, 229, 2869, 43531, 776887, 15953673, 370643273, 9612579511, 275311670611, 8630788777645, 293959006143997, 10809131718965763, 426781883555301359, 18008850183328692241, 808793517812627212561
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=A000312(n)-A000312(n-1).
(12n^2 + 6n + 1)^2 divides a(6n+1), where (12n^2 + 6n + 1) = (2n+1)^3 - (2n)^3{19,61,127,217,331,469,631,817,1027,1261,...} = A127854(n) = A003215(2n) are the hex (or centered hexagonal) numbers. The prime numbers of the form (12n^2 + 6n + 1) belong to A002407 Cuban primes: primes of the form p = (x^3 - y^3 )/(x - y), x=y+1 (prime hex numbers). - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 09 2007
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REFERENCES
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R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see equation (6.7).
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LINKS
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R. K. Hoeflin, Mega Test
Eric Weisstein's World of Mathematics, Power Difference Prime
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FORMULA
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|disc(x^(n+1)-x+1)|.
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EXAMPLE
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a(14) = 10809131718965763 = 3 * 61^2 * 968299894201.
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MATHEMATICA
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a[n_]:=(n+1)^(n+1)-n^n; [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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CROSSREFS
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Cf. A068954, A068955, A068956, A068957, A068146.
Cf. A127854 = Largest number k such that k^2 divides A007781(6n+1). Cf. A003215, A002407.
Sequence in context: A068954 A068955 A151393 this_sequence A068146 A162591 A122009
Adjacent sequences: A007778 A007779 A007780 this_sequence A007782 A007783 A007784
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KEYWORD
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nonn
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AUTHOR
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peter.mccormack(AT)its.csiro.au
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