A250311 Numbers which produce primes if their prime factors, one by one, are prepended, inserted or appended.

49, 131, 133, 149, 151, 157, 169, 173, 179, 191, 197, 199, 223, 233, 239, 247, 277, 281, 283, 293, 313, 331, 337, 361, 367, 383, 397, 401, 409, 419, 421, 431, 439, 443, 457, 463, 467, 469, 481, 503, 547, 553, 571, 577, 587, 589, 607, 641, 643, 659, 673, 679, 701

Offset: 1

Author

Paolo P. Lava, Nov 18 2014

Keywords

• nonn
• base
• easy

Examples

			Prime factors of a(1) = 49 are 7, 7 and concat(4,7,9) = 479 is prime.
a(2) = 131 is prime and concat(13,131,1) = 131311 is prime, as is concat(1,131,31) = 113131.
Prime factors of a(3) = 14383 are 19, 757. Then, concat(1,19,4383) = 1194383 is prime and concat(1438,757,3) = is prime, as is concat(14,757,383) = 14757383.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

CF. A250312.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,c,f,g,h,j,k,n;
for n from 1 by 2 to q do a:=ifactors(n)[2]; h:=0;
for k from 1 to nops(a) do b:=ilog10(a[k][1])+1;
for j from 0 to ilog10(n)+1 do f:=(n mod 10^j);
if j=0 then c:=n*10^b+a[k][1]; else g:=a[k][1]*10^(ilog10(f)+1)+f;
c:=trunc(n/10^j)*10^(ilog10(g)+1)+g; fi;
if isprime(c) then h:=h+1; break; fi; od;
if h=nops(a) then print(n); fi; od; od; end: P(10^6);