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%I #21 Oct 19 2022 10:24:56
%S 2344,172,131,174,52,77,75,83,75,81,89,95,101,104,110,133,143,127,133,
%T 119,124,129,134,139,144,149,154,159,164,169,174,179,184,189,194,199,
%U 204,209,214,219,224,229,234,238,243,248,253,258,263,268,273,278,283
%N The minimal number which has multiplicative persistence 4 in base n.
%C The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. a(3) and a(4) do not seem to exist.
%H Michael De Vlieger, <a href="/A064868/b064868.txt">Table of n, a(n) for n = 5..10000</a>
%H M. R. Diamond and D. D. Reidpath, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/persistence/PERSIST.PDF">A counterexample to a conjecture of Sloane and Erdos</a>, J. Recreational Math., 1998 29(2), 89-92.
%H Sascha Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/persistence/persistence.html">Persistence in different bases</a>
%H T. Lamont-Smith, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Lamont/lamont5.html">Multiplicative Persistence and Absolute Multiplicative Persistence</a>, J. Int. Seq., Vol. 24 (2021), Article 21.6.7.
%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_022.htm">Minimal prime with persistence p</a>
%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence</a>
%F a(n) = 5*n-floor(n/24) for n > 23.
%e a(6) = 172 because 172 = [444]->[144]->[24]->[12]->[2] and no lesser n has persistence 4 in base 6.
%t With[{m = 4, r = 24}, Table[Block[{k = 1}, While[Length@ FixedPointList[Times @@ IntegerDigits[#, n] &, k] != m + 2, k++]; k], {n, m + 1, r}]~Join~Array[(m + 1) # - Floor[#/r] &, 34, r + 1]] (* _Michael De Vlieger_, Aug 30 2021 *)
%o (PARI) pers(nn, b) = {ok = 0; p = 0; until (ok, d = digits(nn, b); if (#d == 1, ok = 1, p++); nn = prod(k=1, #d, d[k]); if (nn == 0, ok = 1);); return (p);}
%o a(n) = {i=0; while (pers(i, n) != 4, i++); return (i);} \\ _Michel Marcus_, Jun 30 2013
%Y Cf. A003001, A031346, A064867, A064869, A064870, A064871, A064872.
%K base,easy,nonn
%O 5,1
%A _Sascha Kurz_, Oct 09 2001
%E Example modified by _Harvey P. Dale_, Oct 19 2022
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