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A046510 Numbers with multiplicative persistence value 1.

%I A046510 #36 Feb 16 2025 08:32:39
%S A046510 10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,30,31,32,33,40,41,42,50,
%T A046510 51,60,61,70,71,80,81,90,91,100,101,102,103,104,105,106,107,108,109,
%U A046510 110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,130,131,132,133
%N A046510 Numbers with multiplicative persistence value 1.
%C A046510 Numbers 0 to 9 have a multiplication persistence of 0, not 1. - _Daniel Mondot_, Mar 12 2022
%H A046510 Daniel Mondot, <a href="/A046510/b046510.txt">Table of n, a(n) for n = 1..10000</a>
%H A046510 N. J. A. Sloane, <a href="http://neilsloane.com/doc/persistence.html">The persistence of a number</a>, J. Recreational Math., 6 (1973), 97-98.
%H A046510 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence</a>
%e A046510 24 -> 2 * 4 = [ 8 ] -> one digit in one step.
%t A046510 Select[Range[10, 121], IntegerLength[Times @@ IntegerDigits[#]] <= 1 &] (* _Jayanta Basu_, Jun 26 2013 *)
%o A046510 (PARI) isok(n) = my(d=digits(n)); (#d > 1) && (#digits(prod(k=1, #d, d[k])) <= 1); \\ _Michel Marcus_, Apr 12 2018 and Mar 13 2022
%o A046510 (Python)
%o A046510 from math import prod
%o A046510 def ok(n): return n > 9 and prod(map(int, str(n))) < 10
%o A046510 print([k for k in range(134) if ok(k)]) # _Michael S. Branicky_, Mar 13 2022
%Y A046510 Cf. A003001, A014120, A046501.
%Y A046510 Numbers with multiplicative persistence m: this sequence (m=1), A046511 (m=2), A046512 (m=3), A046513 (m=4), A046514 (m=5), A046515 (m=6), A046516 (m=7), A046517 (m=8), A046518 (m=9), A352531 (m=10), A352532 (m=11).
%K A046510 nonn,base
%O A046510 1,1
%A A046510 _Patrick De Geest_, Sep 15 1998
%E A046510 Incorrect terms 0 to 9 removed by _Daniel Mondot_, Mar 12 2022