A046424 Numbers requiring 4 steps to reach a prime under the prime factor concatenation procedure.

10, 15, 16, 26, 27, 95, 118, 119, 121, 132, 145, 202, 204, 217, 286, 295, 302, 308, 354, 361, 370, 377, 400, 437, 451, 453, 455, 471, 474, 483, 506, 518, 526, 528, 530, 545, 567, 600, 610, 616, 635, 649, 650, 654, 655, 672, 699, 700, 718, 720, 722, 735, 745

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn
• base

Examples

			95 = 5*19 -> 519 = 3*173 -> 3173 = 19*167 -> 19167 = 3*6389 and 36389 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Patrick De Geest, Home Primes

Crossrefs

Cf. A037271, A046411.

Programs

Maple

filter:= proc(n) local k,F,x,j;
  x:= n;
  for k from 1 to 4 do
    if isprime(x) then return false fi;
    F:= sort(ifactors(x)[2],(a,b) -> a[1] t[1] $ t[2], F);
    x:= F[1];
    for j from 2 to nops(F) do
      x:= x*10^(1+ilog10(F[j]))+F[j]
    od;
  od;
  isprime(x)
end proc:
select(filter, [$2..1000]);# Robert Israel, Jun 25 2019

Extensions

Edited by Charles R Greathouse IV, Apr 28 2010