A164573 Numbers n such that n and n+5 are prime powers.

2, 3, 4, 8, 11, 27, 32, 59, 251, 1019, 2048, 4091, 262139, 1048571, 67108859, 4294967291, 68719476731, 140737488355328, 9007199254740992, 72057594037927931, 73786976294838206459, 332306998946228968225951765070086139

Offset: 1

Author

Daniel Forgues, Aug 16 2009

Keywords

• nonn

Comments

Numbers n such that n + (0, 5) is a prime power pair.

n + (0, 2m), m >= 1, being an admissible pattern for prime pairs, since (0, 2m) = (0, 0) (mod 2), has high density.

n + (0, 2m-1), m >= 1, being a non-admissible pattern for prime pairs, since (0, 2m-1) = (0, 1) (mod 2), has low density [the only possible pairs are (2^a - 2m-1, 2^a) or (2^a, 2^a + 2m-1), a >= 0.]

Numbers n such that n and n+5 are primes would give only 2, for the prime pair (2, 7).

10^18 < a(21) <= 73786976294838206459. - Donovan Johnson, Aug 17 2009

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..37

Crossrefs

Cf. A006549 Numbers n such that n and n+1 are prime powers.

Cf. A120431 Numbers n such that n and n+2 are prime powers.

Cf. A164571 Numbers n such that n and n+3 are prime powers.

Cf. A164572 Numbers n such that n and n+4 are prime powers.

Cf. A164573 Numbers n such that n and n+5 are prime powers.

Cf. A164574 Numbers n such that n and n+6 are prime powers.

Programs

PARI

is(n)=if(n<5,return(n>1)); isprimepower(n) && isprimepower(n+5) \\ Charles R Greathouse IV, Apr 24 2015

PARI

v=List();for(n=0,1e3,if(isprimepower(2^n-5),listput(v,2^n-5));if(isprimepower(2^n+5),listput(v,2^n))); Set(v) \\ Charles R Greathouse IV, Apr 24 2015

Extensions

Edited by Daniel Forgues, Aug 17 2009

a(13)-a(20) from Donovan Johnson, Aug 17 2009

a(21)-a(22) from Charles R Greathouse IV, Apr 24 2015