A336740 Lexicographically earliest sequence of distinct positive terms starting with a(1) = 110 such that the successive sums of the last two digits of the sequence reproduce, digit by digit, the sequence itself.

110, 19, 10, 9, 1, 8, 101, 7, 3, 89, 12, 6, 18, 4, 2, 99, 13, 11, 27, 36, 49, 29, 102, 5, 21, 15, 22, 45, 111, 54, 28, 211, 14, 311, 38, 23, 411, 511, 31, 32, 47, 69, 104, 611, 17, 711, 56, 59, 103, 65, 112, 26, 811, 121, 113, 74, 41, 83, 212, 58, 911, 122, 16, 24, 63, 37, 131, 33, 92, 98, 25, 129, 105, 42

Offset

1,1

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10002

Example

After a(1) = 110 (the sum of the last two digits is 1) the smallest unused term allowing us to reconstruct the sequence by adding its last two digits is a(2) = 19 (1+9 = 10); the succession of the two sums so far is 1, 10;
a(3) = 10, the smallest unused term allowing us to rebuild the sequence by adding its last two digits (1+0 = 1); the succession of the three sums so far is 1, 10, 1;
a(4) = 9, the smallest unused term allowing us to rebuild the sequence by adding its last two digits (0+9 = 9); the succession of the four sums so far is 1, 10, 1, 9;
a(5) = 1, the smallest unused term allowing us to rebuild the sequence by adding its last two digits (9+1 = 10); the succession of the five sums so far is 1, 10, 1, 9, 10 which is precisely the succession of the sequence's digits itself. Etc.

Crossrefs

Cf. A336523 (product instead of sum).

Sequence in context: A282325 A266660 A087303 * A045884 A247391 A110736

Adjacent sequences: A336737 A336738 A336739 * A336741 A336742 A336743

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Aug 02 2020

Status

approved