A064869 The minimal number which has multiplicative persistence 5 in base n.

244140624, 3629, 1601, 1535, 394, 679, 317, 1099, 127, 135, 582, 187, 168, 157, 201, 159, 230, 215, 180, 185, 246, 181, 188, 195, 198, 323, 239, 255, 259, 267, 239, 287, 295, 293, 310, 313, 280, 377, 375, 395, 347, 360, 321, 370, 439, 431, 458, 355, 362

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) seem not 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.

Carlos Rivera, Puzzle 22. Primes and Persistence, The Prime Puzzles and Problems Connection.

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) = 6*n-floor(n/120) for n > 119.

Example

a(9)=394 because 394=[477]->[237]->[46]->[26]->[13]->[3] and no smaller n has persistence 5 in base 9.

Crossrefs

Cf. A003001, A031346, A064867, A064868, A064870, A064871, A064872.

Sequence in context: A335591 A234058 A353554 * A016824 A016860 A016980

Adjacent sequences: A064866 A064867 A064868 * A064870 A064871 A064872

Keyword

base,easy,nonn

Author

Sascha Kurz, Oct 09 2001

Status

approved