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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.
2
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
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
KEYWORD
base,nonn
AUTHOR
STATUS
approved