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

Author

N. J. A. Sloane, Jul 19 2014

Keywords

• nonn

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.

Crossrefs

Cf. A000085. See A264737 for another version.

Programs

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 *)