A213631 Primes p such that primality of (p+p')/2+4 and of (p+p')/2-4 differ, where p'=nextprime(p+1), the next larger prime.

5, 19, 37, 43, 67, 97, 109, 223, 229, 277, 307, 313, 349, 457, 463, 613, 643, 853, 859, 877, 883, 1087, 1093, 1279, 1297, 1303, 1423, 1429, 1447, 1489, 1609, 1663, 1693, 1783, 1867, 1993

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(precprime(p-1)", "))

Crossrefs

Cf. A213632.

Sequence in context: A031041 A029523 A289289 * A242589 A232057 A031093

Adjacent sequences: A213628 A213629 A213630 * A213632 A213633 A213634

Keyword

nonn

Author

M. F. Hasler, Jun 16 2012

Status

approved