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

1,1

Comments

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.

Links

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

Example

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,...

Crossrefs

Cf. A334336.

Sequence in context: A330189 A362027 A358150 * A338288 A330008 A335844

Adjacent sequences: A335211 A335212 A335213 * A335215 A335216 A335217

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, May 27 2020

Status

approved