cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Views

Author

Scott R. Shannon, Feb 16 2025

Keywords

Comments

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

Crossrefs

Cf. A381087, A381183, A011532.

A381183 a(n) = the smallest positive integer that produces a product that contains the digit 2 when multiplied by 2 at most n times, and where a further multiplication by 2 produces a number that does not contain the digit 2. Set a(n) = -1 if no such number exists.

Original entry on oeis.org

2, 1, 6, 31, 128, 64, 516, 331, 814, 1607, 4107, 10158, 10258, 5129, 10283, 12819, 25633, 28141, 16163, 51404, 80134, 80864, 40633, 80216, 40108, 128129, 250627, 160626, 80313, 125641, 208141, 383814, 391628, 195814, 156766, 196314, 391563, 490641, 806166, 785313, 628222, 314111, 625322, 312661, 1563305, 2630104, 1315052, 657526, 328763, 1643815
Offset: 0

Views

Author

Michael De Vlieger and Scott R. Shannon, Feb 16 2025

Keywords

Comments

It is plausible that there are many terms, likely almost all terms, such that a(n) = -1, since the products as n increases become so large it is almost certain that subsequent products also contain the digit 2. It is therefore extremely unlikely that the series of products will terminate for very large values of n. See A381087.
For all starting values up to 10^9 the lowest undetermined term is a(263), while the largest determined term is a(370) = 357131067. The largest term value in this range is a(301) = 957107659.

Examples

			a(2) = 6 as 6*2 = 12, 12*2 = 24, 24*2 = 48, and the first two products contain the digit 2 while the third does not.
a(6) = 516 as 516*2 = 1032, 1032*2 = 2064, 2064*2 = 4128, 4128*2 = 8256, 8256*2 = 16512, 16512*2 = 33024, 33024*2 = 66048, and the first six products contain the digit 2 while the seventh does not.

Links

Crossrefs

Cf. A381087, A378138, A011532.
Showing 1-2 of 2 results.

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