A272816 Prime pairs of the form (p, p+20).

3, 23, 11, 31, 17, 37, 23, 43, 41, 61, 47, 67, 53, 73, 59, 79, 83, 103, 89, 109, 107, 127, 131, 151, 137, 157, 173, 193, 179, 199, 191, 211, 251, 271, 257, 277, 263, 283, 293, 313, 311, 331, 317, 337, 347, 367, 353, 373, 359, 379, 389, 409, 401, 421

Offset: 1

Author

Vincenzo Librandi, May 07 2016

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A153419.

Cf. similar sequences listed in A272815.

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).

Programs

Magma

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

Mathematica

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

Python

from gmpy2 import is_prime
for n in range(1000):
   if(is_prime(n) and is_prime(n+20)):
      print('{}, {}'.format(n,n+20),end=', ')
# Soumil Mandal, May 14 2016

Formula

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

Extensions

Edited by Bruno Berselli, May 12 2016