A377655 - OEIS

%I #12 Nov 04 2024 18:32:48

%S 1093,2,3,30577,7,41,13,43,2633,17,11,23,31,83,233,103,59,97,25037,53,

%T 67,3323,14717

%N 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 For n = 23, 27, 37, 40, 42, ..., a(n) > 5 * 10^9 if not -1.

%C a(23) > 2*10^11 if it is not -1. - _Michael S. Branicky_, Nov 04 2024

%F a(n) = prime(i) where A179077(i) = n, if such i exists.

%e a(4) = 7 because (2^7 - 2)/7 = 18 == 4 (mod 7), and 7 is the first prime that works.

%p f:= p -> (2&^p-2 mod p^2)/p:

%p V:= Array(0..22): count:= 0:

%p p:= 1:

%p for i from 1 while count < 23 do

%p   p:= nextprime(p);

%p   v:= f(p);

%p   if v <= 22 and V[v] = 0 then V[v]:= i; count:= count+1 fi;

%p od:

%p convert(V,list);

%Y Cf. A179077, A377669.

%K nonn,more

%O 0,1

%A _Robert Israel_, Nov 03 2024