A270997 Numbers k such that k | A006190(k-1).

1, 3, 10, 17, 23, 29, 33, 43, 53, 61, 79, 101, 103, 107, 113, 127, 131, 139, 157, 173, 179, 181, 191, 199, 211, 233, 251, 257, 263, 269, 277, 283, 311, 313, 337, 347, 367, 373, 385, 389, 419, 433, 439, 443, 467, 491, 503, 521, 523, 547, 561, 563, 569, 571, 599, 601, 607, 641, 647, 649, 653, 659

Offset: 1

Author

Altug Alkan, Mar 28 2016

Keywords

• nonn

Comments

This sequence appears to generate many prime numbers.

The first few composite terms in this sequence are 10, 33, 385, 561, 649, ...

Contains all members of A038883 except 13. - Robert Israel, Jun 03 2019

That is, contains all primes which are congruent to +-1, +-3 or +-4 (mod 13). - M. F. Hasler, Feb 16 2022

Examples

			10 is a term because A006190(9) = 12970 is divisible by 10.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006190, A038883, A270951.

Programs

Maple

M:= <<3,1>|<1,0>>:
filter:= proc(n) uses LinearAlgebra[Modular];
  local A;
  A:= Mod(n,M,integer);
  MatrixPower(n,A,n-1)[1,2]=0
end proc:
filter(1):= true:
select(filter, [$1..659]); # Robert Israel, Jun 03 2019

Mathematica

nn = 660; s = LinearRecurrence[{3, 1}, {0, 1}, nn]; Select[Range@ nn, Divisible[s[[#]], #] &](* Michael De Vlieger, Mar 28 2016, after Harvey P. Dale at A006190 *)

PARI

a006190(n) = ([1, 3; 1, 2]^n)[2, 1];
for(n=1, 1e3, if(Mod(a006190(n-1), n) == 0, print1(n, ", ")));