%I #32 Jul 23 2023 22:22:04

%S 11,13,17,19,23,31,41,61,71,101,103,107,109,113,131,151,181,191,211,

%T 241,307,311,313,331,401,409,421,503,509,601,607,701,709,809,811,907,

%U 911,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087

%N Primes with multiplicative persistence value 1.

%C The numbers < 10 have persistence 0. - _T. D. Noe_, Nov 23 2011

%C Also: Primes having either at least one digit "0", or any number of digits "1" and product of digits > 1 less than 10 (i.e., among {2, ..., 9, 2*2, 2*3, 2*4, 3*3, 2*2*2}). Terms without a digit "0" and such that deleting some digits "1" never yields an earlier term could be called "primitive". There are only finitely many such elements. If the terms < 10 are ignored, the primitive elements are 11, ..., 71, 151, 181, 211, 241, 313, 421, 811, 911, ... - _M. F. Hasler_, Sep 25 2012

%H Daniel Mondot, <a href="/A046501/b046501.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence</a>

%e 181 -> 1*8*1 = 8; one digit in one step.

%t Select[Prime[Range[179]], IntegerLength[Times @@ IntegerDigits[#]] <= 1 &] (* _Jayanta Basu_, Jun 26 2013 *)

%o (PARI) is_A046501(n)={isprime(n) || return; my(P=n%10); while(P & n\=10, (P*=n%10)>9 & return);1} \\ _M. F. Hasler_, Sep 25 2012

%o (Python)

%o from math import prod

%o from sympy import isprime

%o def ok(n): return n > 9 and prod(map(int, str(n))) < 10 and isprime(n)

%o print([k for k in range(1088) if ok(k)]) # _Michael S. Branicky_, Mar 14 2022

%Y Intersection of A000040 and A046510.

%Y Cf. A046500.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Sep 15 1998

%E Numbers < 10 removed, as they have a multiplicative persistence of 0, by _Daniel Mondot_, Mar 14 2022