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A064868
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The minimal number which has multiplicative persistence 4 in base n.
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11
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2344, 172, 131, 174, 52, 77, 75, 83, 75, 81, 89, 95, 101, 104, 110, 133, 143, 127, 133, 119, 124, 129, 134, 139, 144, 149, 154, 159, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283
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OFFSET
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5,1
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COMMENTS
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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.
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 5..10000
M. R. Diamond and D. D. Reidpath, A counterexample to a conjecture of Sloane and Erdos, J. Recreational Math., 1998 29(2), 89-92.
Sascha Kurz, Persistence in different bases
T. Lamont-Smith, Multiplicative Persistence and Absolute Multiplicative Persistence, J. Int. Seq., Vol. 24 (2021), Article 21.6.7.
C. Rivera, Minimal prime with persistence p
N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.
Eric Weisstein's World of Mathematics, Multiplicative Persistence
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FORMULA
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a(n) = 5*n-floor(n/24) for n > 23.
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EXAMPLE
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a(6) = 172 because 172 = [444]->[144]->[24]->[12]->[2] and no lesser n has persistence 4 in base 6.
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MATHEMATICA
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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 *)
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PROG
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(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); }
a(n) = {i=0; while (pers(i, n) != 4, i++); return (i); } \\ Michel Marcus, Jun 30 2013
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CROSSREFS
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Cf. A003001, A031346, A064867, A064869, A064870, A064871, A064872.
Sequence in context: A023938 A132204 A181129 * A263556 A255099 A216989
Adjacent sequences: A064865 A064866 A064867 * A064869 A064870 A064871
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KEYWORD
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base,easy,nonn
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AUTHOR
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Sascha Kurz, Oct 09 2001
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EXTENSIONS
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Example modified by Harvey P. Dale, Oct 19 2022
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STATUS
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approved
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