

A046501


Primes with multiplicative persistence value 1.


5



11, 13, 17, 19, 23, 31, 41, 61, 71, 101, 103, 107, 109, 113, 131, 151, 181, 191, 211, 241, 307, 311, 313, 331, 401, 409, 421, 503, 509, 601, 607, 701, 709, 809, 811, 907, 911, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087
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OFFSET

1,1


COMMENTS

The numbers < 10 have persistence 0.  T. D. Noe, Nov 23 2011
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


LINKS



EXAMPLE

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


MATHEMATICA

Select[Prime[Range[179]], IntegerLength[Times @@ IntegerDigits[#]] <= 1 &] (* Jayanta Basu, Jun 26 2013 *)


PROG

(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
(Python)
from math import prod
from sympy import isprime
def ok(n): return n > 9 and prod(map(int, str(n))) < 10 and isprime(n)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS

Numbers < 10 removed, as they have a multiplicative persistence of 0, by Daniel Mondot, Mar 14 2022


STATUS

approved



