A334336 -id:A334336 - cp's OEIS frontend

A335214 Divide the biggest term of the pair [a(n), a(n+1)] by the smallest one and keep the remainder; the successive remainders of the successive pairs rebuild the starting sequence, digit after digit. This is the lexicographically earliest sequence of distinct positive terms with this property.

10, 3, 6, 9, 15, 24, 23, 18, 8, 12, 5, 13, 14, 22, 30, 29, 27, 11, 34, 31, 17, 19, 21, 45, 90, 44, 35, 33, 26, 25, 4, 7, 32, 63, 46, 47, 38, 36, 37, 41, 87, 39, 78, 74, 70, 67, 62, 59, 28, 54, 52, 57, 53, 60, 92, 43, 20, 16, 86, 82, 75, 72, 64, 61, 55, 58, 51, 106, 88, 81, 42, 49, 155, 148, 48, 103, 206, 40, 127, 65

Offset: 1

Eric Angelini and Jean-Marc Falcoz, May 27 2020

This is conjectured to be a permutation of the positive integers.

One might enter the successive remainders as the sequence T, which would start with 1, 0, 3, 6, 9, 1, 5, 2, 4, 2, 3, 1, 8, 8, 1, 2, 5, 1, 3, 14, 2, 2, 3, 0, 2, 9, 2, 7, 1, 1, 3, 4, 31, 17, 1, 9,... We see that some remainders are > 9.

			a(1)/a(2) = 10/3 = 3 with remainder 1;
a(3)/a(2) = 6/3 = 2 with remainder 0;
a(4)/a(3) = 9/6 = 1 with remainder 3;
a(5)/a(4) = 15/9 = 1 with remainder 6;
a(6)/a(5) = 24/15 = 1 with remainder 9;
a(6)/a(7) = 24/23 = 1 with remainder 1;
a(7)/a(8) = 23/18 = 1 with remainder 5; etc.
We see that the successive remainders 1,0,3,6,9,1,5,... are the successive digits of the sequence itself 10,3,6,9,15,24,23,...

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Cf. A334336.

A102663 Lexicographically earliest increasing sequence whose k-th digit is the absolute difference between the two digits touching the k-th comma.

Original entry on oeis.org

1, 2, 4, 80, 81, 100, 800, 1000, 1001, 1002, 2000, 8001, 10001, 10002, 10003, 30001, 100001, 100002, 100003, 300001, 1000000, 1000001, 2000001, 10000001, 10000002, 40000000, 200000001, 1000000001, 1000000002, 2000000000, 8000000001, 10000000001, 10000000002

Offset: 1

Eric Angelini and Alexandre Wajnberg, Feb 03 2005

			The first comma is touched by digits 1 and 2 which subtracted absolutely give 1, the first digit of the sequence.
The 2nd comma is touched by digits 2 and 4 which subtracted absolutely give 2, the 2nd digit of the sequence.
The 3rd comma is touched by digits 4 and 8 which subtracted absolutely give 4, the 3rd digit of the sequence.

Cf. A334336.

a(15) corrected and a(16) onwards from Mohammed Yaseen, Jul 10 2021

cp's OEIS Frontend

A335214 Divide the biggest term of the pair [a(n), a(n+1)] by the smallest one and keep the remainder; the successive remainders of the successive pairs rebuild the starting sequence, digit after digit. This is the lexicographically earliest sequence of distinct positive terms with this property.

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