A250312 Numbers which produce primes if their divisors, one by one, are prepended, inserted or appended.

1, 151, 157, 169, 223, 277, 283, 337, 361, 367, 397, 409, 421, 439, 457, 469, 547, 571, 577, 589, 607, 643, 673, 709, 757, 769, 793, 871, 877, 937, 1063, 1093, 1201, 1603, 1609, 1807, 2029, 2053, 2071, 2707, 3019, 3037, 3049, 3073, 3109, 3607, 4039, 4051, 4087

Offset: 1

Author

Paolo P. Lava, Nov 18 2014

Keywords

• nonn
• base
• easy

Examples

			Divisors of 1 is 1 and concat(1,1) = 11 is prime.
Divisors of 151 are 1, 151. Then concat(151,1) = 1511 is prime, as is concat(1,151) = 1151, and concat(1,151,51) = 115151 is prime.
Divisors of 169 are 1, 13, 169. Then concat(16,1,9) = 1619 is prime, concat(16,13,9) = 16139 is prime, as is concat(1,13,69) = 11369, and concat(1,169,69) = 116969 is prime.
		

Links

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

Crossrefs

CF. A250311.

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:=divisors(n); h:=0;
for k from 1 to nops(a) do b:=ilog10(a[k])+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]; else g:=a[k]*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);

Extensions

Inserted a(3), a(16) and a(26) by Paolo P. Lava, Nov 21 2014