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

Author

Jud McCranie

Keywords

• nonn

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

Examples

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

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.

Crossrefs

Contains A074268.

Programs

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