A064867 The minimal number which has multiplicative persistence 3 in base n.

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

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