A034915 Primes of the form p^k - p + 1 for prime p.

3, 7, 31, 43, 79, 127, 157, 241, 337, 727, 1321, 3121, 4423, 6163, 6841, 8191, 19183, 19681, 22651, 26407, 28549, 29761, 37057, 68881, 78121, 113233, 117643, 121453, 130303, 131071, 143263, 208393, 292141, 371281, 375157, 412807, 524287, 527803

Offset

1,1

Comments

Related to hyperperfect numbers of a certain form.

Since x^k-x+1 is divisible by x^2-x+1 for k==2 (mod 6), none of k=8,14,20,... occur. - Robert Israel, Mar 20 2018

Links

Robert Israel, Table of n, a(n) for n = 1..4960

J. S. McCranie, A study of hyperperfect numbers, J. Int. Seqs. Vol. 3 (2000) #P00.1.3.

Example

11^3 - 11 + 1 = 1321 is prime, so 1321 is a term.

Maple

N:= 10^6: # to get all terms <= N
Res:= NULL;
p:= 1:
do
  p:= nextprime(p);
  if p^2-p+1>N then break fi;
  for i from 2 to floor(log[p](N+p-1)) do
    if isprime(p^i-p+1) then Res:= Res, p^i-p+1 fi
  od
od:
sort(convert({Res}, list)); # Robert Israel, Mar 20 2018

Crossrefs

Contains A074268.

Sequence in context: A110581 A128436 A213899 * A145479 A077315 A365423

Adjacent sequences: A034912 A034913 A034914 * A034916 A034917 A034918

Keyword

nonn

Author

Jud McCranie

Status

approved