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A125598
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a(n) = ((n+1)^(n-1) - 1)/n.
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3
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0, 1, 5, 31, 259, 2801, 37449, 597871, 11111111, 235794769, 5628851293, 149346699503, 4361070182715, 139013933454241, 4803839602528529, 178901440719363487, 7143501829211426575, 304465936543600121441
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OFFSET
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1,3
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COMMENTS
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Odd prime p divides a(p-2).
a(n) is prime for n = {3,4,6,74, ...}; prime terms are {5, 31, 2801, ...}.
a(n) is the (n-1)-th generalized repunit in base (n+1). For example, a(5) = 259 which is 1111 in base 6. - Mathew Englander, Oct 20 2020
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LINKS
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FORMULA
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a(n) = ((n+1)^(n-1) - 1)/n.
a(2k-1)/(2k+1) = A125599(k) for k>0.
For n > 1, a(n) = Sum_{k=0..n-2} (n+1)^k.
For n > 1, a(n) = Sum_{j=0..n-2} n^j*C(n-1,j+1). (End)
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MATHEMATICA
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Table[((n+1)^(n-1)-1)/n, {n, 25}]
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PROG
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(Sage) [gaussian_binomial(n, 1, n+2) for n in range(0, 18)] # Zerinvary Lajos, May 31 2009
(Magma) [((n+1)^(n-1) -1)/n: n in [1..25]]; // G. C. Greubel, Aug 15 2022
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CROSSREFS
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Cf. other sequences of generalized repunits, such as A125118, A053696, A055129, A060072, A031973, A173468, A023037, A119598, A085104, and A162861.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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