A245177 Inefficient primes.

5, 13, 19, 23, 29, 31, 43, 53, 59, 61, 67, 73, 79, 83, 89, 97, 103, 131, 137, 151, 157, 163, 173, 179, 181, 191, 197, 199, 211, 229, 233, 239, 241, 281, 293, 307, 317, 347, 359, 367, 373, 379, 389, 397, 409, 419, 421, 431, 433, 443, 449

Offset

1,1

Comments

A prime p is inefficient (see Amdeberhan - Moll) if it divides A000085(n) for some n < p.

Links

Robert Israel, Table of n, a(n) for n = 1..1428

Tewodros Amdeberhan and Victor H. Moll, Involutions and their progenies, preprint, 2014.

Tewodros Amdeberhan and Victor H. Moll, Involutions and their progenies, arXiv:1406.2356 [math.CO], 2014.

Tewodros Amdeberhan and Victor H. Moll, Involutions and their progenies, Journal of Combinatorics, 6(4) (2015), 483-508.

Maple

N:= 1000:  # to get all terms <= N
I1:= proc(n) option remember;  I1(n-1)+(n-1)*I1(n-2) end proc:
I1(0):= 1: I1(1):= 1:
Primes:= select(isprime, {2, seq(2*i+1, i=1..floor((N-1)/2))}):
PP:= convert(Primes, `*`):
A:= {}:
for n from 1 to N-1 do
  g:= igcd(I1(n), PP):
  A:= A union select(`>`, numtheory:-factorset(g), n);
od:
A; # Robert Israel, Jul 20 2014

Mathematica

A85 = DifferenceRoot[Function[{y, n}, {(-n-1) y[n] - y[n+1] + y[n+2] == 0, y[1] == 1, y[2] == 2}]];
inefficientQ[p_] := AnyTrue[Range[p-1], Divisible[A85[#], p]&];
Reap[For[p = 2, p < 1000, p = NextPrime[p], If[inefficientQ[p], Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Jul 28 2020 *)

Crossrefs

Cf. A000085. See A264737 for another version.

Sequence in context: A226193 A028274 A272723 * A067463 A209663 A156111

Adjacent sequences: A245174 A245175 A245176 * A245178 A245179 A245180

Keyword

nonn

Author

N. J. A. Sloane, Jul 19 2014

Status

approved