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

1,2

Links

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

Example

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.

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);

Crossrefs

CF. A250311.

Sequence in context: A115483 A182875 A336777 * A180554 A243531 A139505

Adjacent sequences: A250309 A250310 A250311 * A250313 A250314 A250315

Keyword

nonn,base,easy

Author

Paolo P. Lava, Nov 18 2014

Extensions

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

Status

approved