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

1,1

Links

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

Example

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.

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);

Crossrefs

CF. A250312.

Sequence in context: A202331 A044300 A044681 * A211727 A304674 A257524

Adjacent sequences: A250308 A250309 A250310 * A250312 A250313 A250314

Keyword

nonn,base,easy

Author

Paolo P. Lava, Nov 18 2014

Status

approved