A164572 Numbers k such that k and k+4 are both prime powers.

1, 3, 4, 5, 7, 9, 13, 19, 23, 25, 27, 37, 43, 49, 67, 79, 97, 103, 109, 121, 127, 163, 169, 193, 223, 229, 239, 277, 289, 307, 313, 343, 349, 379, 397, 439, 457, 463, 487, 499, 613, 643, 673, 729, 739, 757, 769, 823, 853, 859, 877, 883, 907, 937, 967, 1009, 1087

Offset

1,2

Comments

Numbers n such that n + (0, 4) is a prime power pair.

A generalization of the cousin primes. The cousin primes are a subsequence.

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.]

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1256 from Daniel Forgues)

Mathematica

Select[Range[1000], PrimeNu[#] < 2 && PrimeNu[# + 4] < 2 &] (* Amiram Eldar, Oct 01 2020 *)

Prog

(PARI) is(n)=if(n==1, return(1)); isprimepower(n) && isprimepower(n+4) \\ Charles R Greathouse IV, Apr 24 2015

Crossrefs

Cf. A023200, A000961.

k and (x) are prime powers: A006549 (k+1), A120431 (k+2), A164571 (k+3), this sequence (k+4), A164573 (k+5), A164574 (k+6).

Sequence in context: A226918 A227391 A209721 * A067530 A259796 A082922

Adjacent sequences: A164569 A164570 A164571 * A164573 A164574 A164575

Keyword

nonn

Author

Daniel Forgues, Aug 16 2009, Aug 17 2009

Status

approved