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A256344 Moduli n for which A248218(n) = 4 (length of the terminating cycle of 0 under x -> x^2+1 modulo n).

%I A256344 #11 Mar 09 2021 20:15:17
%S A256344 13,26,39,47,52,78,79,91,94,104,113,141,143,156,158,169,173,182,188,
%T A256344 197,208,226,237,247,273,282,286,299,312,316,329,338,339,346,353,364,
%U A256344 376,377,394,403,416,429,439,452,474,481,494,507,517,519,546,553,559,564,572,591,598
%N A256344 Moduli n for which A248218(n) = 4 (length of the terminating cycle of 0 under x -> x^2+1 modulo n).
%C A256344 If x is a member and y is a member of this sequence or A248219 or A256342, then LCM(x,y) is a member. - _Robert Israel_, Mar 09 2021
%H A256344 Robert Israel, <a href="/A256344/b256344.txt">Table of n, a(n) for n = 1..10000</a>
%e A256344 See A256342 or A256349.
%p A256344 filter:= proc(n) local x, k, R,p;
%p A256344   x:= 0; R[0]:= 0;
%p A256344   for k from 1 do
%p A256344     x:= x^2+1 mod n;
%p A256344     if assigned(R[x]) then return evalb(k-R[x] = 4)
%p A256344     else R[x]:= k
%p A256344     fi
%p A256344   od;
%p A256344 end proc:
%p A256344 select(filter, [$1..1000]); # _Robert Israel_, Mar 09 2021
%o A256344 (PARI) for(i=1,600,A248218(i)==4&&print1(i","))
%Y A256344 Cf. A248218, A248219, A256342 - A256349, A003095, A247981.
%K A256344 nonn
%O A256344 1,1
%A A256344 _M. F. Hasler_, Mar 25 2015