A381183 -id:A381183 - cp's OEIS frontend

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

Scott R. Shannon, Feb 13 2025

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.

			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.

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

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

A378138 The distinct values, in order of appearance, of A381087.

Original entry on oeis.org

2, 1, 6, 31, 64, 331, 814, 1607, 4107, 5129, 10283, 12819, 16163, 40108, 80313, 100153, 256379, 1281895, 2571143, 3130008

Offset: 0

Scott R. Shannon, Feb 16 2025

See A381087 for further details. It is plausible, although unproven, that 3130008 is the final term.

Cf. A381087, A381183, A011532.

cp's OEIS Frontend

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

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