A090123 Integers k such that nextprime(k^5) - prevprime(k^5) = 4.

411, 741, 819, 4041, 6165, 6315, 6861, 10281, 11025, 12489, 12579, 13119, 14331, 15225, 16095, 19125, 19881, 19929, 20799, 22461, 24051, 24885, 25815, 25971, 26979, 27075, 29955, 30801, 31641, 32661, 37371, 38361, 39369, 41181, 42681

Offset

1,1

Links

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

Example

For k = 411, k^5 = 11727599043051; nextprime(k^5) - prevprime(k^5) = 11727599043053 - 11727599043049 = 4, so k 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=5; Do[If[Equal[Prime[PrimePi[n^k]+1]-Prime[PrimePi[n^k]], 4], Print[n]], {n, 2, 100000}]
np4Q[n_]:=Module[{c=n^5}, NextPrime[c]-NextPrime[c, -1]==4]; Select[ Range[ 43000], np4Q] (* Harvey P. Dale, Oct 06 2017 *)

Prog

(PARI) isok(n) = (nextprime(n^5+1) - precprime(n^5-1)) == 4; \\ Michel Marcus, May 25 2018

Crossrefs

Cf. A077038, A058043, A090121, A090122, A090124, A090125.

Sequence in context: A374270 A212710 A187991 * A055018 A201844 A105211

Adjacent sequences: A090120 A090121 A090122 * A090124 A090125 A090126

Keyword

nonn

Author

Labos Elemer, Jan 12 2004

Extensions

Wrong term 1 removed by Michel Marcus, May 25 2018

Status

approved