A272816 - OEIS

%I #37 Sep 08 2022 08:46:16

%S 3,23,11,31,17,37,23,43,41,61,47,67,53,73,59,79,83,103,89,109,107,127,

%T 131,151,137,157,173,193,179,199,191,211,251,271,257,277,263,283,293,

%U 313,311,331,317,337,347,367,353,373,359,379,389,409,401,421

%N Prime pairs of the form (p, p+20).

%C p and p+20 are not necessarily consecutive primes: (887, 907) is the first pair of consecutive primes that belongs to the sequence.

%H Seiichi Manyama, <a href="/A272816/b272816.txt">Table of n, a(n) for n = 1..10000</a>

%F a(2n+1) = A153419(n+1).

%e The prime pairs are (3, 23), (11, 31), (17, 37) etc.

%t Flatten[{#, # + 20}&/@Select[Prime[Range[200]], PrimeQ[# + 20] &]]

%o (Magma) &cat [[p, p+20]: p in PrimesUpTo(1000) | IsPrime(p+20)];

%o (Python)

%o from gmpy2 import is_prime

%o for n in range(1000):

%o    if(is_prime(n) and is_prime(n+20)):

%o       print('{}, {}'.format(n,n+20),end=', ')

%o # _Soumil Mandal_, May 14 2016

%Y Cf. A000040, A153419.

%Y Cf. similar sequences listed in A272815.

%Y Prime pairs of the form (p, p+k): A077800 (k=2), A094343 (k=4), A156274 (k=6), A156320 (k=8), A140445 (k=10), A156323 (k=12), A140446 (k=14), A272815 (k=16), A156328 (k=18), this sequence (k=20), A140447 (k=22).

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, May 07 2016

%E Edited by _Bruno Berselli_, May 12 2016