A381087 The smallest positive integer that produces a product that contains the digit 2 when multiplied by 2 a total of n times.

2, 1, 6, 31, 64, 64, 331, 331, 814, 1607, 4107, 5129, 5129, 5129, 10283, 12819, 16163, 16163, 16163, 40108, 40108, 40108, 40108, 40108, 40108, 80313, 80313, 80313, 80313, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153, 100153

Offset: 0

Author

Scott R. Shannon, Feb 13 2025

Keywords

• nonn
• base

Comments

The last known distinct term is a(148) = 3130008; all subsequent terms studied also equal 3130008, and it is plausible, although unproven, that this is the last distinct value as n -> infinity.

Examples

			a(2) = 6 as 6*2 = 12 and 12*2 = 24, and the two products contain the digit 2.
a(8) = 814 as 814*2 = 1628, 1628*2 = 3256, 3256*2 = 6512, 6512*2 = 13024, 13024*2 = 26048, 26048*2 = 52096, 52096*2 = 104192, 104192*2 = 208384, and the eight products contain the digit 2.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A378138 (distinct values), A381183, A011532.