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

1,1

Comments

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

Links

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

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.

Example

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.

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 *)

Crossrefs

Cf. A000085. Essentially a duplicate of A245177.

Sequence in context: A235204 A354706 A348392 * A045364 A045365 A104491

Adjacent sequences: A264734 A264735 A264736 * A264738 A264739 A264740

Keyword

nonn,easy

Author

David Eppstein, Nov 22 2015

Status

approved