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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 29 03:03 EST 2023. Contains 367422 sequences. (Running on oeis4.)