

A164572


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


7



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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, 2m1), m >= 1, being a nonadmissible pattern for prime pairs, since (0, 2m1) = (0, 1) (mod 2), has low density [the only possible pairs are (2^a  2m1, 2^a) or (2^a, 2^a + 2m1), 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



