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A034915 Primes of the form p^k - p + 1 for prime p. 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified April 19 19:02 EDT 2024. Contains 371798 sequences. (Running on oeis4.)