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A214785 Numbers k such that k + 6 = A214783(k).

%I A214785 #22 Jun 09 2023 08:54:30
%S A214785 7,13,17,53,67,97,137,157,167,193,227,257,293,313,317,383,397,457,463,
%T A214785 503,547,577,587,593,643,653,673,683,727,757,773,823,827,883,887,937,
%U A214785 997,1013,1063,1093,1163,1213,1237
%N A214785 Numbers k such that k + 6 = A214783(k).
%C A214785 This set is disjoint from A213784. Conjecture: all terms are prime.
%H A214785 Robert Israel, <a href="/A214785/b214785.txt">Table of n, a(n) for n = 1..5000</a>
%p A214785 f:= proc(n) local a,b,t,T,k;
%p A214785   b:= 0; a:= 1; T:= -3 mod n;
%p A214785   for k from 1 do
%p A214785     t:= a+b mod n;
%p A214785     if t = T then return k+1 fi;
%p A214785     a:= b; b:= t;
%p A214785   od
%p A214785 end proc:
%p A214785 f(1):= 1: f(3):= 1:
%p A214785 select(n -> f(n) = n+6, [$1..2000]); # _Robert Israel_, Jun 08 2023
%Y A214785 Cf. A214783, A214784.
%K A214785 nonn
%O A214785 1,1
%A A214785 _Art DuPre_, Aug 03 2012