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.

1093, 2, 3, 30577, 7, 41, 13, 43, 2633, 17, 11, 23, 31, 83, 233, 103, 59, 97, 25037, 53, 67, 3323, 14717

Offset

0,1

Comments

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

a(23) > 2*10^11 if it is not -1. - Michael S. Branicky, Nov 04 2024

Links

Table of n, a(n) for n=0..22.

Formula

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

Example

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

Maple

f:= p -> (2&^p-2 mod p^2)/p:
V:= Array(0..22): count:= 0:
p:= 1:
for i from 1 while count < 23 do
  p:= nextprime(p);
  v:= f(p);
  if v <= 22 and V[v] = 0 then V[v]:= i; count:= count+1 fi;
od:
convert(V, list);

Crossrefs

Cf. A179077, A377669.

Sequence in context: A240719 A239875 A091673 * A288097 A281001 A271100

Adjacent sequences: A377652 A377653 A377654 * A377656 A377657 A377658

Keyword

nonn,more

Author

Robert Israel, Nov 03 2024

Status

approved