A219546 Schenker primes.

5, 13, 23, 31, 37, 41, 43, 47, 53, 59, 61, 71, 79, 101, 103, 107, 109, 127, 137, 149, 157, 163, 173, 179, 181, 191, 197, 199, 211, 223, 229, 241, 251, 257, 263, 271, 277, 283, 293, 311, 317, 337, 349, 353, 359, 367, 383, 397, 401, 409, 419, 421, 431, 439, 461

Offset

1,1

Comments

Amdeberhan, Callan, and Moll (2012) call a prime p a Schenker prime if p divides A063170(r) (the r-th Schenker sum with n-th term) for some r < p.

For any non-Schenker prime p, Amdeberhan, Callan, and Moll (2012) give a formula for the p-adic valuation of any Schenker sum with n-th term.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..783

T. Amdeberhan, D. Callan, and V. Moll, p-adic analysis and combinatorics of truncated exponential sums, preprint, 2012.

T. Amdeberhan, D. Callan and V. Moll, Valuations and combinatorics of truncated exponential sums, INTEGERS 13 (2013), #A21.

Example

5 is a Schenker prime because 2 < 5 and 5 divides A063170(2) = 10.
17 is not a Schenker prime because 17 is not a factor of A063170(1) = 2, or of A063170(2) = 10, . . . , or of A063170(16) = 105224992014096760832.

Mathematica

pmax = 300; A063170 = Table[n!*Sum[n^k/k!, {k, 0, n}], {n, 1, pmax}]; Rest[Select[Table[If[PrimeQ[j] && SelectFirst[Range[j], Divisible[A063170[[#]], j] &] != j, j, 0], {j, 1, pmax}], # != 0 &]] (* Vaclav Kotesovec, Nov 30 2017 *)

Crossrefs

Cf. A063170.

Sequence in context: A006353 A155142 A155552 * A143988 A129806 A125830

Adjacent sequences: A219543 A219544 A219545 * A219547 A219548 A219549

Keyword

nonn

Author

Jonathan Sondow, Nov 22 2012

Extensions

More terms from Vaclav Kotesovec, Nov 30 2017

Status

approved