A219546 - OEIS

%I #17 Dec 21 2020 02:04:02

%S 5,13,23,31,37,41,43,47,53,59,61,71,79,101,103,107,109,127,137,149,

%T 157,163,173,179,181,191,197,199,211,223,229,241,251,257,263,271,277,

%U 283,293,311,317,337,349,353,359,367,383,397,401,409,419,421,431,439,461

%N Schenker primes.

%C 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.

%C 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.

%H Vaclav Kotesovec, <a href="/A219546/b219546.txt">Table of n, a(n) for n = 1..783</a>

%H T. Amdeberhan, D. Callan, and V. Moll, <a href="http://dauns.math.tulane.edu/~vhm/papers_html/schenker.pdf">p-adic analysis and combinatorics of truncated exponential sums</a>, preprint, 2012.

%H T. Amdeberhan, D. Callan and V. Moll, <a href="http://www.emis.de/journals/INTEGERS/papers/n21/n21.Abstract.html">Valuations and combinatorics of truncated exponential sums</a>, INTEGERS 13 (2013), #A21.

%e 5 is a Schenker prime because 2 < 5 and 5 divides A063170(2) = 10.

%e 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.

%t 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 *)

%Y Cf. A063170.

%K nonn

%O 1,1

%A _Jonathan Sondow_, Nov 22 2012

%E More terms from _Vaclav Kotesovec_, Nov 30 2017