A103523 Concatenations of pairs of primes that differ by 100.

3103, 7107, 13113, 31131, 37137, 67167, 73173, 79179, 97197, 127227, 139239, 151251, 157257, 163263, 181281, 193293, 211311, 283383, 331431, 349449, 367467, 379479, 409509, 421521, 457557, 463563, 487587, 499599, 541641, 547647, 577677

Offset

1,1

Comments

Integers in this sequence can never be prime, as, starting from the second one, they are all multiples of 3.

Links

Robert Israel, Table of n, a(n) for n = 1..9832

Formula

List: concatenate(p, p+100) iff p and p+100 are primes.

Example

9191019 is in this sequence because 919 is prime, 919+100 = 1019 is prime and 9191019 is the concatenation of those two primes differing by 100.

Maple

f:= proc(n) if isprime(n) and isprime(n+100) then 10^(1+ilog10(n+100))*n+n+100 fi end proc:
map(f, [3, seq(i, i=7..1000, 6)]); # Robert Israel, Dec 07 2015

Mathematica

FromDigits[Join@@IntegerDigits/@{#, #+100}]&/@Select[Prime@Range@200, PrimeQ[#+100]&] (* Giorgos Kalogeropoulos, Jul 04 2021 *)

Prog

(Python)
from sympy import isprime, primerange as prange
def auptop(lim):
  return [int(str(p)+str(p+100)) for p in prange(2, lim+1) if isprime(p+100)]
print(auptop(577)) # Michael S. Branicky, Jul 04 2021

Crossrefs

Cf. A000040, A001358, A023201, A100750, A103195, A103206, A104718, A104719.

Sequence in context: A187305 A236121 A252884 * A345519 A234265 A090056

Adjacent sequences: A103520 A103521 A103522 * A103524 A103525 A103526

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Mar 21 2005

Status

approved