A265684 Sarrus numbers (A001567) that are the average of two consecutive primes.

645, 7957, 11305, 15841, 25761, 35333, 126217, 194221, 212421, 332949, 464185, 635401, 656601, 741751, 934021, 1193221, 1357441, 1459927, 1620385, 1690501, 1969417, 2704801, 3911197, 4154161, 4209661, 5095177, 5284333, 5351537, 5758273, 6189121, 6212361, 7820201, 8134561, 8209657

Offset

1,1

Comments

Inspired by A265669.

Motivation was the form of differences between consecutive primes that generate this sequence. It seems that 12*k appears in differences most of the time. For the first 175 term of this sequence, the relevant proportion is 161/175.

Differences between corresponding consecutive primes are 4, 12, 12, 36, 4, 12, 12, 36, 4, 4, 24, 24, 4, 60, 24, 24, 24, 12, 12, 36, 12, 24, 12, 24, 36, 12, 12, 12, 12, 24, 4, 60, 24, 48, 36, 12, 24, 36, 24, 20, 12, 84, 36, 12, 24, 24, 12, 24, 36, 12, 12, 36, ...

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

645 is a term because it is a Sarrus number and the average of the consecutive primes 643 and 647.
7957 is a term because it is a Sarrus number and the average of the consecutive primes 7951 and 7963.

Mathematica

Select[Range[200000], CompositeQ[#] && PowerMod[2, (# - 1), #] == 1 && NextPrime[#] - # == # - NextPrime[#, -1] &] (* Amiram Eldar, Jun 28 2019 *)

Prog

(PARI) is(n)={Mod(2, n)^n==2 && !isprime(n)}
forcomposite(n=2, 1e7, if(is(n) && (nextprime(n)-n)==(n-precprime(n)), print1(n, ", ")))

Crossrefs

Intersection of A001567 and A024675.

Cf. A265669.

Sequence in context: A227136 A216364 A063844 * A067845 A057942 A230488

Adjacent sequences: A265681 A265682 A265683 * A265685 A265686 A265687

Keyword

nonn

Author

Altug Alkan, Dec 13 2015

Status

approved