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A007781
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(n+1)^(n+1) - n^n.
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10
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1, 3, 23, 229, 2869, 43531, 776887, 15953673, 370643273, 9612579511, 275311670611, 8630788777645, 293959006143997, 10809131718965763, 426781883555301359, 18008850183328692241, 808793517812627212561
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see equation (6.7).
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LINKS
| R. K. Hoeflin, Mega Test
Eric Weisstein's World of Mathematics, Power Difference Prime
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FORMULA
| |disc(x^(n+1)-x+1)|.
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EXAMPLE
| a(14) = 10809131718965763 = 3 * 61^2 * 968299894201.
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MATHEMATICA
| Join[{1}, Table[(n+1)^(n+1)-n^n, {n, 20}]] (* From Harvey P. Dale, Feb. 09 2011 *)
Differences[Table[n^n, {n, 0, 20}]] (* From Charles R Greathouse IV, Feb 09 2011 *)
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CROSSREFS
| Cf. A068954, A068955, A068956, A068957, A068146, A003215, A002407.
Cf. A127854 = Largest number k such that k^2 divides A007781(6n+1).
Sequence in context: A068954 A068955 A151393 * A068146 A162591 A122009
Adjacent sequences: A007778 A007779 A007780 * A007782 A007783 A007784
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KEYWORD
| nonn,easy
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AUTHOR
| peter.mccormack(AT)its.csiro.au
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