cp's OEIS Frontend

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

%I A270997 #21 Feb 17 2022 00:28:11
%S A270997 1,3,10,17,23,29,33,43,53,61,79,101,103,107,113,127,131,139,157,173,
%T A270997 179,181,191,199,211,233,251,257,263,269,277,283,311,313,337,347,367,
%U A270997 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
%N A270997 Numbers k such that k | A006190(k-1).
%C A270997 This sequence appears to generate many prime numbers.
%C A270997 The first few composite terms in this sequence are 10, 33, 385, 561, 649, ...
%C A270997 Contains all members of A038883 except 13. - _Robert Israel_, Jun 03 2019
%C A270997 That is, contains all primes which are congruent to  +-1, +-3 or +-4 (mod 13). - _M. F. Hasler_, Feb 16 2022
%H A270997 Robert Israel, <a href="/A270997/b270997.txt">Table of n, a(n) for n = 1..10000</a>
%e A270997 10 is a term because A006190(9) = 12970 is divisible by 10.
%p A270997 M:= <<3,1>|<1,0>>:
%p A270997 filter:= proc(n) uses LinearAlgebra[Modular];
%p A270997   local A;
%p A270997   A:= Mod(n,M,integer);
%p A270997   MatrixPower(n,A,n-1)[1,2]=0
%p A270997 end proc:
%p A270997 filter(1):= true:
%p A270997 select(filter, [$1..659]); # _Robert Israel_, Jun 03 2019
%t A270997 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 *)
%o A270997 (PARI) a006190(n) = ([1, 3; 1, 2]^n)[2, 1];
%o A270997 for(n=1, 1e3, if(Mod(a006190(n-1), n) == 0, print1(n, ", ")));
%Y A270997 Cf. A006190, A038883, A270951.
%K A270997 nonn
%O A270997 1,2
%A A270997 _Altug Alkan_, Mar 28 2016