A262668 Numbers n such that n-19, n-1, n+1 and n+19 are consecutive primes.

20982, 28182, 51768, 57222, 76422, 87720, 90678, 104850, 108108, 110730, 141180, 199602, 227112, 248118, 264600, 268842, 304392, 304458, 320082, 322920, 330018, 382728, 401670, 414432, 429972, 450258, 467082, 489408, 520548, 535608, 540120

Offset

1,1

Comments

This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.

The terms ending in 0 are divisible by 30 (cf. A249674).

The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.

Links

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

Eric Weisstein's World of Mathematics, Twin Primes

Example

20982 is the average of the four consecutive primes 20963, 20981, 20983, 21001.
28182 is the average of the four consecutive primes 28163, 28181, 28183, 28201.

Mathematica

Select[Range[6, 600000, 6], And[AllTrue[{# - 1, # + 1}, PrimeQ], NextPrime[# - 1, -1] == # - 19, NextPrime[# + 1] == # + 19] &] (* Michael De Vlieger, Sep 27 2015, Version 10 *)
Select[Prime@Range@60000, NextPrime[#, {1, 2, 3}] == {18, 20, 38} + # &] + 19 (* Vincenzo Librandi, Oct 10 2015 *)
Mean/@Select[Partition[Prime[Range[50000]], 4, 1], Differences[#]=={18, 2, 18}&] (* Harvey P. Dale, Jan 16 2019 *)

Prog

(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 1000001, 6):
..if isprime(i-1) and isprime(i+1):
....if prevprime(i-1) == i-19 and nextprime(i+1) == i+19 : print(i, end=', ')

Crossrefs

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

Sequence in context: A188104 A278903 A233649 * A344354 A344355 A231314

Adjacent sequences: A262665 A262666 A262667 * A262669 A262670 A262671

Keyword

nonn

Author

Karl V. Keller, Jr., Sep 26 2015

Status

approved