0,2

p divides a(p-1) for prime p = {2, 5, 13, 37, 463, ...} which apparently coincides with A064384(n) = {2, 5, 13, 37, 463, ...} Primes p such that p divides 0!-1!+2!-3!+...+(-1)^{p-1}(p-1)!. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 14 2007

GCD(a(n), a(n+2)) = A124779(n) is either 1 or a prime 2, 5, 13, 37, 463, ... = A064384. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jun 12 2007

For proofs of Adamchuk's and my Comments, see the link "The Taylor series for e ...". - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jun 18 2007

J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.

J. Sondow, The Taylor series for e and the primes 2, 5, 13, 37, 463, ...: a surprising connection

Index entries for sequences related to factorial numbers

J. Sondow, Which Partial Sums of the Taylor Series for e Are Convergents to e? (and a Link to the Primes $2, 5, 13, 37, 463, ...$) with an Appendix "Periodic Behaviour of Some Recurrence Sequences Related to $e$, Modulo Powers of 2" by Kyle Schalm

Numerators of floor(n!*exp(1))/n!, n>=1. Numerators of coefficients in expansion of exp(x)/(1-x). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 11 2002

(1+n+n(n-1)+...+n!)/GCD(n!,1+n+n(n-1)+...+n!) - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 18 2006

1, 2, 5/2, 8/3, 65/24, 163/60, 1957/720, 685/252, ...

Cf. A061355, A093101.

a(n) = A000522(n)/A093101(n).

Cf. A064384.

Cf. A064384, A124779, A129924.

Sequence in context: A086809 A130378 A120342 this_sequence A011039 A021390 A019802

Adjacent sequences: A061351 A061352 A061353 this_sequence A061355 A061356 A061357

nonn,frac

Amarnath_murthy (amarnath_murthy(AT)yahoo.com), Apr 28 2001