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.

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

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 *)
Select[Partition[Prime[Range[700]], 4, 1], #[[3]]-#[[2]]==2&&(#[[1]]+#[[4]])/2 == (#[[2]]+#[[3]])/2&][[All, 2]]+1 (* Harvey P. Dale, May 06 2022 *)

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