%I #19 Jun 09 2024 09:04:59
%S 2,3,21,34,46,87,99,129,141,220,242,254,266,278,279,476,526,550,616,
%T 627,657,772,777,783,795,1072,1088,1322,1442,1486,1540,1552,1586,1653,
%U 1725,1833,1959,1994,2001,2043,2068,2192,2224,2360,2384,2432,2734,2770,2866
%N Numbers k such that nextprime(k^4) - prevprime(k^4) = 4.
%H Amiram Eldar, <a href="/A090122/b090122.txt">Table of n, a(n) for n = 1..10000</a>
%e For k = 21: k^4 = 194481, q = nextprime(k^4) = 194483, p = prevprime(k^4) = 194479, q - p = 4, so 21 is in the sequence.
%t pre[x_] := Prime[PrimePi[x]]; nex[x_] := Prime[PrimePi[x]+1]; de[x_] := Prime[PrimePi[x]+1]-Prime[PrimePi[x]]; k=4; Do[If[Equal[Prime[PrimePi[n^k]+1]-Prime[PrimePi[n^k]], 4], Print[n]], {n, 2, 100000}]
%o (PARI) is(k) = nextprime(k^4 + 1) - precprime(k^4 - 1) == 4; \\ _Amiram Eldar_, Jun 09 2024
%Y Cf. A077038, A058043, A090123, A090124, A090125.
%K nonn
%O 1,1
%A _Labos Elemer_, Jan 12 2004
%E a(29)-a(49) from _Giovanni Resta_, May 08 2017