A139313 - OEIS

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A139313

Primes prime(n) such that -prime(n-1) + 3*prime(n) - 3*prime(n+1) + prime(n+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

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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

LINKS

Table of n, a(n) for n=1..47.

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}]]