A281924 - OEIS

%I #7 Feb 17 2017 08:28:32

%S 23,11,11,13,5,317,5,29,3,-1,3,11,19,293,5,7,17,239,3,-1,11,241,5,3,3,

%T 227,5,19,7,-1,7,41,7,853,5,17,7,29,3,-1,5,31,11,3,3,37,5,29,7,-1,11,

%U 61,7,13,13,47,13,19,3,-1,5,821,5,3,3,47,11,29,3,-1,3,11

%N Least prime p such that p*n is a concatenation of two primes, -1 if it does not exist.

%C If p*n = concat(a,b), leading 0 in b are admitted.

%C a(n) = -1 if a(n) mod 10 = 0.

%H Paolo P. Lava, <a href="/A281924/b281924.txt">Table of n, a(n) for n = 1..2500</a>

%e a(1) = 23 because 23*1 = 23 = concat(2,3);

%e a(2) = 11 because 11*2 = 22 = concat(2,2);

%e a(6) = 317 because 317^6 = 1902 = concat(19,02).

%p with(numtheory): P:= proc(q) local a,k,n,ok;

%p for n from 1 to q do for a from 1 by 2 to q do if isprime(a) then ok:=0;

%p for k from 1 to ilog10(a*n) do if isprime(trunc(a*n/10^k)) and isprime(a*n mod 10^k) then ok:=1; break; fi; od; if ok=1 then print(a); break; fi; fi; od; od; end: P(10^9);

%Y Cf. A000040, A281923.

%K sign,base,easy

%O 1,1

%A _Paolo P. Lava_, Feb 16 2017