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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..36.

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

Cf A213631.

Sequence in context: A143030 A031043 A183126 * A031095 A319050 A031371

Adjacent sequences:  A213629 A213630 A213631 * A213633 A213634 A213635

KEYWORD

nonn

AUTHOR

M. F. Hasler, Jun 16 2012

STATUS

approved

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Last modified July 25 16:39 EDT 2021. Contains 346291 sequences. (Running on oeis4.)