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A227064
Primes prime(k) such that the gap prime(k-1) - prime(k-2) equals the gap prime(k+2) - prime(k+1).
2
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
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
Sequence in context: A098029 A098039 A132237 * A143030 A031043 A183126
KEYWORD
nonn,less
AUTHOR
EXTENSIONS
Corrected by R. J. Mathar, Jul 12 2013
STATUS
approved