A125582 Smallest positive integer with multiplicative persistence n in base 12.

1, 12, 30, 46, 83, 1099, 1571, 17902874277

Offset

0,2

Comments

The sequence in base 12 is 1, 10, 26, 3X, 6E, 777, XXE, 3577777799, where X is 10 and E is 11. I have searched numbers up to 24 digits in base 12 excluding any numbers that might contain the digit 1 or any combination of digits that might multiply to 0 mod 12. The numbers also had digits in nondecreasing order, so that XXE would be tested but, for example, EXX would not.

Links

Table of n, a(n) for n=0..7.

Example

a(0)=1 since 1 is the smallest positive integer for which no multiplication takes place. [Edited by A.H.M. Smeets, Sep 16 2018]
a(6)=1571 since 1571, 1100, 392, 128, 80, 48, 0 is the chain with six multiplications. In base 12, XXE, 778, 288, X8, 68, 40, 0.

Maple

Maple program available upon request.

Mathematica

With[{s = Array[-1 + Length@ FixedPointList[Times @@ IntegerDigits[#, 12] &, #] &, 1600]}, Array[FirstPosition[s, #][[1]] &, Max@ s]] (* Michael De Vlieger, Sep 18 2018 *)

Crossrefs

Cf. A003001, A031346, A046510, A064867, A064868, A064869, A064870, A064871, A064872.

Sequence in context: A298077 A135502 A256620 * A031107 A019557 A173107

Adjacent sequences: A125579 A125580 A125581 * A125583 A125584 A125585

Keyword

more,nonn,base

Author

Walter Kehowski, Jan 04 2007

Status

approved