

A256753


Numbers n such that n is both the average of some twin prime pair p, q (q = p+2) (i.e., n = p+1 = q1) and is also the average of the prime before p and the prime after q.


18



12, 18, 30, 42, 60, 102, 108, 228, 270, 312, 420, 462, 570, 600, 858, 882, 1050, 1092, 1230, 1290, 1302, 1428, 1488, 1620, 1872, 1998, 2028, 2340, 2550, 2688, 2730, 3390, 3462, 3540, 3582, 4020, 4230, 4242, 4272, 4338, 4518, 4650, 4788
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OFFSET

1,1


COMMENTS

This sequence is a subsequence of A014574 (average of twin prime pairs).


LINKS

Karl V. Keller, Jr., Table of n, a(n) for n = 1..500000
Eric Weisstein's World of Mathematics, Twin Primes


EXAMPLE

For n=12: 7, 11, 13, 17 are four consecutive primes with 13 = 11 + 2 and (7+17)/2 = 12.
For n=18: 13, 17, 19, 23 are four consecutive primes with 19 = 17 + 2 and (13+23)/2 = 18.


MATHEMATICA

Select[Prime[Range[10^3]], PrimeQ[#+2]&&2*#+2==NextPrime[#, 1]+NextPrime[#, 2]&]+1 (* Ivan N. Ianakiev, Apr 23 2015 *)


PROG

(Python)
from sympy import isprime, prevprime, nextprime
for i in range(5, 12001, 2):
..if isprime(i) and isprime(i+2):
....if prevprime(i)+nextprime(i, 2) == 2*(i+1): print(i+1, end=', ')
(PARI) lista(nn) = {forprime(p=3, nn, if (isprime(p+2), if (precprime(p1)+nextprime(p+3) == 2*(p+1), print1(p+1, ", ")); ); ); } \\ Michel Marcus, Apr 12 2015


CROSSREFS

Cf. A077800 (twin primes), A014574.
Sequence in context: A112054 A225576 A275082 * A167597 A138636 A075281
Adjacent sequences: A256750 A256751 A256752 * A256754 A256755 A256756


KEYWORD

nonn


AUTHOR

Karl V. Keller, Jr., Apr 09 2015


STATUS

approved



