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A213632
Primes p such that primality of (p+p')/2+4 and of (p+p')/2-4 differ, where p'=precprime(p-1), the next smaller prime.
1
7, 23, 41, 47, 71, 101, 113, 227, 233, 281, 311, 317, 353, 461, 467, 617, 647, 857, 863, 881, 887, 1091, 1097, 1283, 1301, 1307, 1427, 1433, 1451, 1493, 1613, 1667, 1697, 1787, 1871, 1997
OFFSET
1,1
COMMENTS
It is easily checked that for m=(p+p')/2 (average between two consecutive primes), the numbers m +- 1 resp. m +- 2 resp. m +- 3 (as well as m +- 6) are (in each case) either both prime or both composite (for p > 7). Thus, m +- 4 provides the least counterexample to this behavior, and the primes listed here are those for which the property does not hold, i.e., one among { m-4, m+4 } is prime and the other one is composite.
PROG
(PARI) d=8; q=3; forprime(p=nextprime(q+1), q+1999, [1, -1]*isprime([q-d+p; q+d+q=p]\2) & print1(p", "))
CROSSREFS
Sequence in context: A143030 A031043 A183126 * A031095 A375352 A319050
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jun 16 2012
STATUS
approved