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A377655 a(n) is the least prime p such that (2^p - 2)/p == n (mod p), or -1 if there is no such prime p.

%I A377655 #12 Nov 04 2024 18:32:48
%S A377655 1093,2,3,30577,7,41,13,43,2633,17,11,23,31,83,233,103,59,97,25037,53,
%T A377655 67,3323,14717
%N A377655 a(n) is the least prime p such that (2^p - 2)/p == n (mod p), or -1 if there is no such prime p.
%C A377655 For n = 23, 27, 37, 40, 42, ..., a(n) > 5 * 10^9 if not -1.
%C A377655 a(23) > 2*10^11 if it is not -1. - _Michael S. Branicky_, Nov 04 2024
%F A377655 a(n) = prime(i) where A179077(i) = n, if such i exists.
%e A377655 a(4) = 7 because (2^7 - 2)/7 = 18 == 4 (mod 7), and 7 is the first prime that works.
%p A377655 f:= p -> (2&^p-2 mod p^2)/p:
%p A377655 V:= Array(0..22): count:= 0:
%p A377655 p:= 1:
%p A377655 for i from 1 while count < 23 do
%p A377655   p:= nextprime(p);
%p A377655   v:= f(p);
%p A377655   if v <= 22 and V[v] = 0 then V[v]:= i; count:= count+1 fi;
%p A377655 od:
%p A377655 convert(V,list);
%Y A377655 Cf. A179077, A377669.
%K A377655 nonn,more
%O A377655 0,1
%A A377655 _Robert Israel_, Nov 03 2024