This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A164572 #16 Oct 01 2020 03:24:25 %S A164572 1,3,4,5,7,9,13,19,23,25,27,37,43,49,67,79,97,103,109,121,127,163,169, %T A164572 193,223,229,239,277,289,307,313,343,349,379,397,439,457,463,487,499, %U A164572 613,643,673,729,739,757,769,823,853,859,877,883,907,937,967,1009,1087 %N A164572 Numbers k such that k and k+4 are both prime powers. %C A164572 Numbers n such that n + (0, 4) is a prime power pair. %C A164572 A generalization of the cousin primes. The cousin primes are a subsequence. %C A164572 n + (0, 2m), m >= 1, being an admissible pattern for prime pairs, since (0, 2m) = (0, 0) (mod 2), has high density. %C A164572 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.] %H A164572 Amiram Eldar, <a href="/A164572/b164572.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1256 from Daniel Forgues) %t A164572 Select[Range[1000], PrimeNu[#] < 2 && PrimeNu[# + 4] < 2 &] (* _Amiram Eldar_, Oct 01 2020 *) %o A164572 (PARI) is(n)=if(n==1,return(1)); isprimepower(n) && isprimepower(n+4) \\ _Charles R Greathouse IV_, Apr 24 2015 %Y A164572 Cf. A023200, A000961. %Y A164572 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). %K A164572 nonn %O A164572 1,2 %A A164572 _Daniel Forgues_, Aug 16 2009, Aug 17 2009