



29, 1439, 4211, 7703, 12907, 14957, 16703, 20947, 29221, 31189, 33053, 36749, 44531, 51437, 90247, 115547, 124783, 127163, 133337, 144511, 146449, 151339, 157133, 166219, 169241, 180233, 181031, 185123, 197383, 223367, 225287, 240347
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OFFSET

1,1


COMMENTS

Primes that are the arithmetic mean of two consecutive balanced primes (of order one); primes of the form A006562(k)+A006562(k+1))/2.
Might be called prime interprimes of order two.


LINKS

Table of n, a(n) for n=1..32.


MATHEMATICA

b = {}; a = {}; Do[If[PrimeQ[((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2], AppendTo[a, ((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2]], {n, 1, 10000}]; Do[If[PrimeQ[(a[[k + 1]] + a[[k]])/2], AppendTo[b, (a[[k + 1]] + a[[k]])/2]], {k, 1, Length[a]  1}]; b


PROG

(PARI) {m=250000; a=0; p=2; q=3; r=5; while(r<=m, if((p+r)/2==q, if(a>0, if(isprime(b=(a+q)/2), print1(b, ", "))); a=q); p=q; q=r; r=nextprime(r+1))}  Klaus Brockhaus, Jan 05 2007


CROSSREFS

Cf. A126554, A006562.
Sequence in context: A191968 A049657 A091994 * A028478 A042627 A042624
Adjacent sequences: A126552 A126553 A126554 * A126556 A126557 A126558


KEYWORD

nonn


AUTHOR

Artur Jasinski, Dec 27 2006


EXTENSIONS

Edited and extended by Klaus Brockhaus, Jan 05 2007


STATUS

approved



