A090122 Numbers k such that nextprime(k^4) - prevprime(k^4) = 4.

2, 3, 21, 34, 46, 87, 99, 129, 141, 220, 242, 254, 266, 278, 279, 476, 526, 550, 616, 627, 657, 772, 777, 783, 795, 1072, 1088, 1322, 1442, 1486, 1540, 1552, 1586, 1653, 1725, 1833, 1959, 1994, 2001, 2043, 2068, 2192, 2224, 2360, 2384, 2432, 2734, 2770, 2866

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

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}]

Prog

(PARI) is(k) = nextprime(k^4 + 1) - precprime(k^4 - 1) == 4; \\ Amiram Eldar, Jun 09 2024

Crossrefs

Cf. A077038, A058043, A090123, A090124, A090125.

Sequence in context: A024765 A282340 A248953 * A328734 A296254 A114749

Adjacent sequences: A090119 A090120 A090121 * A090123 A090124 A090125

Keyword

nonn

Author

Labos Elemer, Jan 12 2004

Extensions

a(29)-a(49) from Giovanni Resta, May 08 2017

Status

approved