A214785 - OEIS

%I #22 Jun 09 2023 08:54:30

%S 7,13,17,53,67,97,137,157,167,193,227,257,293,313,317,383,397,457,463,

%T 503,547,577,587,593,643,653,673,683,727,757,773,823,827,883,887,937,

%U 997,1013,1063,1093,1163,1213,1237

%N Numbers k such that k + 6 = A214783(k).

%C This set is disjoint from A213784. Conjecture: all terms are prime.

%H Robert Israel, <a href="/A214785/b214785.txt">Table of n, a(n) for n = 1..5000</a>

%p f:= proc(n) local a,b,t,T,k;

%p   b:= 0; a:= 1; T:= -3 mod n;

%p   for k from 1 do

%p     t:= a+b mod n;

%p     if t = T then return k+1 fi;

%p     a:= b; b:= t;

%p   od

%p end proc:

%p f(1):= 1: f(3):= 1:

%p select(n -> f(n) = n+6, [$1..2000]); # _Robert Israel_, Jun 08 2023

%Y Cf. A214783, A214784.

%K nonn

%O 1,1

%A _Art DuPre_, Aug 03 2012