A075764 - OEIS

%I #23 Jun 28 2022 02:57:23

%S 105,261,301,693,1605,1755,2151,2905,2907,3393,3875,4641,4833,5005,

%T 5655,6279,6913,7161,8883,9405,10899,11025,11289,15687,17199,19203,

%U 22275,27387,36855,37791,50007,50463,53493,54891,55209,55755,63327,64337

%N Schroeder pseudoprimes: Composites k that divide the k-th Schroeder number A001003(k-1).

%H Amiram Eldar, <a href="/A075764/b075764.txt">Table of n, a(n) for n = 1..422</a>

%e 105 is a term because A001003(105) = 15646506064359350392347086201481965698808674470977505246623827696393838448345 which is divisible by 105.

%e 105 is a term because A001003(104) = 15646506064359350392347086201481965698808674470977505246623827696393838448345 which is divisible by 105.

%t s = {}; k1 = k2 = 1; Do[k3 = ((6*n - 9)*k2 - (n - 3)*k1)/n; If[CompositeQ[n] && Divisible[k3, n], AppendTo[s, n]]; k1 = k2; k2 = k3, {n, 3, 10^5}]; s (* _Amiram Eldar_, Jun 28 2022 *)

%o (PARI) x1 = 1; x2 = 1; for (n = 3, 100000, x = (3*(2*n - 3)*x1 - (n - 3)*x2)/n; if (!isprime(n), if (!(x%n), print(n))); x2 = x1; x1 = x); \\ _David Wasserman_, Feb 23 2005

%Y Intersection of A002808 and A075763.

%Y Cf. A001003, A013998, A075762.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Oct 09 2002

%E More terms from _David Wasserman_, Feb 23 2005