

A213632


Primes p such that primality of (p+p')/2+4 and of (p+p')/24 differ, where p'=precprime(p1), 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
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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 { m4, 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([qd+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



