A064868 The minimal number which has multiplicative persistence 4 in base n.

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

Offset

5,1

Comments

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.

Links

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

Formula

a(n) = 5*n-floor(n/24) for n > 23.

Example

a(6) = 172 because 172 = [444]->[144]->[24]->[12]->[2] and no lesser n has persistence 4 in base 6.

Mathematica

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 *)

Prog

(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

Crossrefs

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

Keyword

base,easy,nonn

Author

Sascha Kurz, Oct 09 2001

Extensions

Example modified by Harvey P. Dale, Oct 19 2022

Status

approved