A356443 Primes p such that the concatenation of p and 2*p is the average of a twin prime pair.

569, 661, 1249, 1559, 1571, 1949, 1999, 2389, 2441, 2609, 2879, 3761, 3911, 5689, 5701, 5749, 5779, 6389, 6481, 6971, 7559, 7561, 7741, 8191, 8971, 9221, 9391, 9521, 10061, 10111, 10289, 10601, 10949, 11821, 11941, 12071, 12281, 12689, 12721, 12809, 13151, 13469, 13681, 14821, 15569, 16931, 18661

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 1249 is a term because 2*1249 = 2498 and 12492498 is the average of the twin prime pair 12492497, 12492499.

Maple

filter:= proc(p) local r;
  if not isprime(p) then return false fi;
  r:= p*10^(1+ilog10(2*p))+2*p;
  isprime(r+1) and isprime(r-1)
end proc:
select(filter, [seq(seq(10*i+j, j=[1, 9]), i=1..10000)]);

Mathematica

Select[Prime[Range[2200]], And @@ PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[2*#]]] + {-1, 1}] &] (* Amiram Eldar, Aug 07 2022 *)

Prog

(Python)
from sympy import isprime
def ok(n):
    if not isprime(n): return False
    t = int(str(n)+str(2*n))
    return isprime(t-1) and isprime(t+1)
print([k for k in range(20000) if ok(k)]) # Michael S. Branicky, Aug 07 2022

Crossrefs

Cf. A014574.

Sequence in context: A290868 A214140 A192822 * A142818 A103818 A240715

Adjacent sequences: A356440 A356441 A356442 * A356444 A356445 A356446

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Aug 07 2022

Status

approved