A046501 Primes with multiplicative persistence value 1.

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

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

Daniel Mondot, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Multiplicative Persistence

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)
print([k for k in range(1088) if ok(k)]) # Michael S. Branicky, Mar 14 2022

Crossrefs

Intersection of A000040 and A046510.

Cf. A046500.

Sequence in context: A046117 A240900 A091923 * A050719 A217062 A293662

Adjacent sequences: A046498 A046499 A046500 * A046502 A046503 A046504

Keyword

nonn,base

Author

Patrick De Geest, Sep 15 1998

Extensions

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

Status

approved