A262668 - OEIS

%I #15 Jan 16 2019 14:56:00

%S 20982,28182,51768,57222,76422,87720,90678,104850,108108,110730,

%T 141180,199602,227112,248118,264600,268842,304392,304458,320082,

%U 322920,330018,382728,401670,414432,429972,450258,467082,489408,520548,535608,540120

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

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

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

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

%H Karl V. Keller, Jr., <a href="/A262668/b262668.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>

%e 20982 is the average of the four consecutive primes 20963, 20981, 20983, 21001.

%e 28182 is the average of the four consecutive primes 28163, 28181, 28183, 28201.

%t 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 *)

%t Select[Prime@Range@60000, NextPrime[#, {1, 2, 3}] == {18, 20, 38} + # &] + 19 (* _Vincenzo Librandi_, Oct 10 2015 *)

%t Mean/@Select[Partition[Prime[Range[50000]],4,1],Differences[#]=={18,2,18}&] (* _Harvey P. Dale_, Jan 16 2019 *)

%o (Python)

%o from sympy import isprime,prevprime,nextprime

%o for i in range(0,1000001,6):

%o ..if isprime(i-1) and isprime(i+1):

%o ....if prevprime(i-1) == i-19 and nextprime(i+1) == i+19 : print(i,end=', ')

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

%K nonn

%O 1,1

%A _Karl V. Keller, Jr._, Sep 26 2015