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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. 1
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 (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(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

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Last modified September 23 12:43 EDT 2021. Contains 347617 sequences. (Running on oeis4.)