A333594 Lexicographically earliest sequence of distinct positive integers such that the decimal expansion of neither a(n)/a(n+1) nor a(n+1)/a(n) contains a significant digit present in either a(n) or a(n+1), with a(1) = 7.

7, 14, 42, 28, 84, 77, 9, 18, 5, 3, 2, 6, 8, 4, 11, 40, 12, 400, 22, 24, 72, 44, 36, 16, 48, 30, 20, 60, 33, 37, 45, 15, 50, 150, 54, 66, 55, 82, 75, 25, 220, 32, 288, 96, 396, 88, 64, 192, 576, 640, 480, 80, 160, 360, 63, 70, 21, 700, 140, 420, 126, 4158, 154, 462, 1540, 518, 1188, 444, 74, 90, 27, 81, 165, 495, 297, 99

Offset

1,1

Comments

By "significant digit" we mean to exclude from the quotients any zeros preceding the first nonzero digit, as well as zeros following the last nonzero digit (as in a terminating decimal).

Is the sequence infinite?

Links

Carole Dubois, Table of n, a(n) for n = 1..300

Example

a(1)/a(2) = 7/14 = .5 and a(2)/a(1) = 14/7 = 2 and their combined distinct significant digits (2,5) are exclusive of the combined distinct digits of a(1) and a(2), (1,4,7).
a(5)/a(6) = 84/77 = 1.090909... and a(6)/a(5) = 77/84 = .916666... and their combined distinct significant digits (0,1,6,9) are exclusive of the combined distinct digits of a(5) and a(6), (4,7,8).
a(299)/a(300) = 656/21648 = .03030303... and a(300)/a(299) = 21648/656 = 33 and their combined distinct significant digits (0,3) is exclusive of the combined distinct digits of a(299) and a(300), (1,2,4,5,6,8).

Crossrefs

Cf. A333480 (where a(1) = 2).

Sequence in context: A304143 A055780 A161814 * A067048 A189046 A098328

Adjacent sequences: A333591 A333592 A333593 * A333595 A333596 A333597

Keyword

base,nonn

Author

Carole Dubois and Eric Angelini, Mar 27 2020

Status

approved