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A139313
Primes prime(n) such that -prime(n-1) + 3*prime(n) - 3*prime(n+1) + prime(n+2) = 0.
1
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[ -1 + n] + 2 Prime[n] - Prime[1 + n] = 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
FORMULA
a(n)=A000040(1+A064149(n)). - R. J. Mathar, Jun 10 2008
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
KEYWORD
nonn,changed
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