A264737 Primes which divide some term of A000085 (numbers of involutions).

2, 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, 457, 461, 463, 479, 487, 491, 499

Offset: 1

Author

David Eppstein, Nov 22 2015

Keywords

• nonn
• easy

Comments

Essentially the same as A245177. - R. J. Mathar, Nov 25 2015

Examples

			23 divides A000085(11) = 35696 = 2^4 * 23 * 97, so it appears in this set. The sequence A000085 mod 3 cycles: 1,1,2,1,1,2,..., so the prime factor 3 does not appear in this set.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A000085. Essentially a duplicate of A245177.

Programs

Maple

filter:= proc(p) local a,b,c,n,R;
  if not isprime(p) then return false fi;
  a:= 1; b:= 1;
  R[1,1,1]:= 1;
  for n from 2 do
    c:= a + (n-1)*b mod p;
    if c = 0 then return true fi;
    b:= a; a:= c;
    if R[a,b,(n mod p)] = 1 then return false fi;
    R[a,b,(n mod p)]:= 1;
  od:
end proc:
select(filter, [2,seq(i,i=3..1000,2)]); # Robert Israel, Nov 22 2015

Mathematica

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

Formula

Any individual prime p is easily tested for membership in this set by iterating the recurrence for A000085 mod p, T(n) = T(n-1) + (n-1)T(n-2) modulo p, until either finding a value divisible by p or entering a cycle.