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

1,2

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A006190, A038883, A270951.

Sequence in context: A043405 A296219 A063293 * A356058 A342280 A024981

Adjacent sequences: A270994 A270995 A270996 * A270998 A270999 A271000

Keyword

nonn

Author

Altug Alkan, Mar 28 2016

Status

approved