A260959 Numbers n such that n is the average of four consecutive primes n-13, n-1, n+1 and n+13.

7950, 10500, 32970, 33330, 34470, 36900, 43050, 66360, 71550, 74610, 87120, 89070, 92400, 94560, 95190, 102000, 104310, 121950, 125790, 133980, 148470, 156900, 160710, 168630, 174930, 182640, 194070, 204600, 206250, 230340, 244380, 246510

Offset

1,1

Comments

This is a subsequence of A014574 (average of twin prime pairs), A256753 and A249674 (30n).

Links

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Twin Primes

Example

7950 is the average of the four consecutive primes 7937, 7949, 7951, 7963.
10500 is the average of the four consecutive primes 10487, 10499, 10501, 10513.

Prog

(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 300001, 2):
.. if isprime(i-1) and isprime(i+1):
....if prevprime(i-1) == i-13 and nextprime(i+1) == i+13 :  print (i, end=', ')
(Perl) use ntheory ":all"; say join ", ", map { $_+1 } grep { next_prime($_+2)-$_==14 } grep { $_-prev_prime($_)==12 } @{twin_primes(1e6)}; # Dana Jacobsen, Oct 03 2015

Crossrefs

Cf. A014574, A077800 (twin primes), A249674, A256753.

Sequence in context: A162010 A023322 A064246 * A316906 A316907 A293623

Adjacent sequences: A260956 A260957 A260958 * A260960 A260961 A260962

Keyword

nonn

Author

Karl V. Keller, Jr., Aug 06 2015

Status

approved