%I #29 Jul 05 2021 02:42:12

%S 3103,7107,13113,31131,37137,67167,73173,79179,97197,127227,139239,

%T 151251,157257,163263,181281,193293,211311,283383,331431,349449,

%U 367467,379479,409509,421521,457557,463563,487587,499599,541641,547647,577677

%N Concatenations of pairs of primes that differ by 100.

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

%H Robert Israel, <a href="/A103523/b103523.txt">Table of n, a(n) for n = 1..9832</a>

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

%e 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.

%p f:= proc(n) if isprime(n) and isprime(n+100) then 10^(1+ilog10(n+100))*n+n+100 fi end proc:

%p map(f, [3,seq(i,i=7..1000,6)]); # _Robert Israel_, Dec 07 2015

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

%o (Python)

%o from sympy import isprime, primerange as prange

%o def auptop(lim):

%o return [int(str(p)+str(p+100)) for p in prange(2, lim+1) if isprime(p+100)]

%o print(auptop(577)) # _Michael S. Branicky_, Jul 04 2021

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

%K base,easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Mar 21 2005