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 A064867 The minimal number which has multiplicative persistence 3 in base n. 11
 26, 63, 68, 23, 27, 31, 35, 39, 43, 46, 50, 54, 58, 62, 66, 69, 73, 77, 81, 85, 89, 92, 96, 100, 104, 108, 112, 115, 119, 123, 127, 131, 135, 138, 142, 146, 150, 154, 158, 161, 165, 169, 173, 177, 181, 184, 188, 192 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. LINKS Michael De Vlieger, Table of n, a(n) for n = 3..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 FORMULA a(n) = 4*n-floor(n/6) for n > 5. EXAMPLE a(3) = 26 because 26 = [222]->[22]->[11]->[1] and no fewer n has persistence 3 in base 3. MATHEMATICA With[{m = 3}, Table[Block[{k = 1}, While[Length@ FixedPointList[Times @@ IntegerDigits[#, n] &, k, 100] != m + 2, k++]; k], {n, 3, 5}]]~Join~Array[4 # - Floor[#/6] &, 45, 6] (* Michael De Vlieger, Aug 30 2021 *) CROSSREFS Cf. A003001, A031346, A064868, A064869, A064870, A064871, A064872. Sequence in context: A043236 A044016 A321023 * A228512 A250605 A020155 Adjacent sequences: A064864 A064865 A064866 * A064868 A064869 A064870 KEYWORD base,easy,nonn AUTHOR Sascha Kurz, Oct 08 2001 STATUS approved

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Last modified July 24 02:45 EDT 2024. Contains 374575 sequences. (Running on oeis4.)