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A264737 Primes which divide some term of A000085 (numbers of involutions). 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jul 28 2020 *)

CROSSREFS

Cf. A000085. Essentially a duplicate of A245177.

Sequence in context: A112634 A303281 A235204 * A045364 A045365 A104491

Adjacent sequences:  A264734 A264735 A264736 * A264738 A264739 A264740

KEYWORD

nonn,easy,changed

AUTHOR

David Eppstein, Nov 22 2015

STATUS

approved

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Last modified August 4 06:22 EDT 2020. Contains 336201 sequences. (Running on oeis4.)