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

Author

Karl V. Keller, Jr., Sep 26 2015

Keywords

• nonn

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.

Examples

			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.
		

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Twin Primes

Crossrefs

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

Programs

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 *)

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=', ')