A227064 Primes prime(k) such that the gap prime(k-1) - prime(k-2) equals the gap prime(k+2) - prime(k+1).

7, 23, 37, 59, 67, 71, 73, 89, 163, 167, 233, 241, 269, 277, 367, 379, 389, 449, 479, 557, 569, 587, 599, 601, 631, 743, 751, 757, 809, 967, 983, 1009, 1033, 1039, 1109, 1117, 1229, 1283, 1297, 1307, 1361, 1439, 1523, 1559, 1607, 1609, 1613, 1637, 1669

Offset

1,1

Comments

This rephrases patterns of the form g, *, *, g in four successive entries of A001223, where * denotes arbitrary, not necessarily distinct, values.

The associated indices are n = 4, 9, 12, 17, 19, 20, 21, 24, 38, ...

Each entry is the second next prime after A022887(n). - R. J. Mathar, Jul 12 2013

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Formula

Prime(k) such that A001223(k-2) = A001223(k+1).

Example

7 is in the sequence since the gap between the previous two primes (3 and 5) is equal to the gap between the next two primes (11 and 13).

Prog

(Python) from sympy import sieve as p
print([p[k] for k in range(3, 264) if p[k-1] - p[k-2] == p[k+2] - p[k+1]])
# Karl-Heinz Hofmann, May 04 2022

Crossrefs

Cf. A001223, A022887.

Sequence in context: A098029 A098039 A132237 * A143030 A031043 A183126

Adjacent sequences: A227061 A227062 A227063 * A227065 A227066 A227067

Keyword

nonn,less

Author

Juri-Stepan Gerasimov, Jun 30 2013

Extensions

Corrected by R. J. Mathar, Jul 12 2013

Status

approved