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A046501 Primes with multiplicative persistence value 1. 4
2, 3, 5, 7, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

According to Eric Weisstein, 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

Table of n, a(n) for n=1..52.

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

CROSSREFS

Cf. A046500, A046510.

Sequence in context: A229060 A219528 A341660 * A033875 A105581 A258433

Adjacent sequences:  A046498 A046499 A046500 * A046502 A046503 A046504

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Sep 15 1998

STATUS

approved

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Last modified March 8 02:09 EST 2021. Contains 341934 sequences. (Running on oeis4.)