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
Examples
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.
Links
- Jean-Marc Falcoz, Table of n, a(n) for n = 1..10002
Crossrefs
Cf. A336523 (product instead of sum).