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 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 = q-1) 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 (list; graph; refs; listen; history; text; internal format)
 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(p-1)+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

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Last modified April 23 06:08 EDT 2019. Contains 322381 sequences. (Running on oeis4.)