

A213631


Primes p such that primality of (p+p')/2+4 and of (p+p')/24 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 { 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(precprime(p1)", "))


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



