A139313 Primes prime(k) such that -prime(k-1) + 3*prime(k) - 3*prime(k+1) + prime(k+2) = 0.

19, 37, 43, 67, 83, 229, 257, 277, 349, 353, 383, 443, 479, 571, 613, 643, 677, 683, 719, 751, 1033, 1093, 1279, 1297, 1429, 1433, 1489, 1553, 1609, 1621, 1663, 1733, 1747, 1783, 1867, 1987, 1993, 2053, 2137, 2207, 2377, 2467, 2503, 2579, 2683, 2689, 2693

Offset

1,1

Comments

If A006562 is when -prime(k-1) + 2*prime(k) - prime(k+1) = 0; then this "Integer differential" is the next higher order.

a(n) = prime(A064149(n)+1), where prime = A000040. - M. F. Hasler, Oct 15 2024

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n)=A000040(1+A064149(n)). - R. J. Mathar, Jun 10 2008

Maple

P:= select(isprime, [2, seq(i, i=3..10000, 2)]):
DP:= P[2..-1]-P[1..-2]:
D2:= DP[2..-1]-DP[1..-2]:
P3:= D2[2..-1]-D2[1..-2]:
J:= select(i -> P3[i]=0, [$1..nops(P3)]):
P[J+~1]; # Robert Israel, Dec 15 2024

Mathematica

Flatten[Table[If[ -Prime[ -1 +n] + 3*Prime[n] - 3*Prime[1 + n] + Prime[n + 2] == 0, Prime[n], {}], {n, 2, 500}]]
Select[Partition[Prime[Range[500]], 4, 1], 3#[[2]]+#[[4]]==#[[1]]+3#[[3]]&][[All, 2]](* Harvey P. Dale, Jul 09 2018 *)

Crossrefs

Cf. A006562.

Cf. A036264 (3rd differences of primes), A064149 (indices of zeros in A036264).

Sequence in context: A059695 A134196 A217045 * A272205 A347371 A332756

Adjacent sequences: A139310 A139311 A139312 * A139314 A139315 A139316

Keyword

nonn

Author

Roger L. Bagula, Jun 07 2008

Extensions

Edited by N. J. A. Sloane, Jul 01 2008

Definition corrected by Harvey P. Dale, Jul 09 2018

Status

approved