A046503 Primes with multiplicative persistence value 3.

47, 59, 79, 89, 97, 139, 149, 157, 179, 193, 197, 227, 229, 239, 263, 283, 293, 337, 347, 353, 359, 367, 373, 383, 389, 419, 433, 443, 449, 463, 479, 487, 491, 499, 571, 577, 593, 619, 643, 661, 673, 683, 691, 719, 733, 743, 751, 757, 797, 823, 829, 839

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base

Examples

			47 -> 4 * 7 -> [ 28 ] -> 2 * 8 -> [ 16 ] -> 1 * 6 -> [ 6 ] -> one digit in three steps.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Multiplicative Persistence

Crossrefs

Cf. A046500, A046512.

Programs

Maple

filter:= proc(n) local L;
  if not isprime(n) then return false fi;
  L:= convert(convert(n,base,10),`*`); if L < 10 then return false fi;
  L:= convert(convert(L,base,10),`*`); if L < 10 then return false fi;
  L:= convert(convert(L,base,10),`*`); evalb(L < 10)
end proc:
select(filter, [seq(i,i=11..1000,2)]); # Robert Israel, Jun 05 2018

Mathematica

pr3Q[n_] := Length[NestWhileList[Times @@ IntegerDigits[#] &, n, # > 9 &]] == 4; Select[Prime[Range[147]], pr3Q] (* Jayanta Basu, Jun 26 2013 *)