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

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

Offset: 0

Author

Walter Kehowski, Jan 04 2007

Keywords

• more
• nonn
• base

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.

Examples

			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.
		

Crossrefs

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

Programs

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 *)