A336523 Lexicographically earliest sequence of distinct positive terms starting with a(1) = 0 and a(2) = 1 such that the product of the last two digits of the sequence rebuilds, digit after digit, the sequence itself.
0, 1, 11, 111, 211, 311, 411, 26, 511, 611, 3, 711, 27, 811, 34, 16, 15, 911, 28, 1011, 1111, 13, 17, 1211, 43, 71, 8, 1311, 1411, 31, 4, 44, 35, 19, 1511, 62, 18, 25, 1611, 1711, 1811, 1911, 2011, 2111, 2211, 113, 2311, 7, 126, 2411, 72, 131, 117, 29, 2511, 213, 2611, 2711, 127, 2811, 2911, 231, 172, 2
Offset: 1
Examples
After a(1) = 0 and a(2) = 1, the smallest unused term a(3) allowing the rebuilding of the sequence by multiplying its last two digits is 11 (1*1 = 1); now the succession of such products is 0, 1; after a(3) = 11, the smallest unused term a(4) allowing the rebuilding of the sequence by multiplying its last two digits is 111 (as the product of the last two digits of 111 is 1*1 = 1); now the succession of the products is 0, 1, 1); after a(4) = 111, the smallest unused term a(5) allowing the rebuilding of the sequence by multiplying its last two digits is 211 (as the product of the last two digits of 211 is 1*1 = 1); now the succession of the products is 0, 1, 1, 1); after a(5) = 211, the smallest unused term a(6) allowing the rebuilding of the sequence by multiplying its last two digits is 311 (as the product of the last two digits of 311 is 1*1 = 1); now the succession of the products is 0, 1, 1, 1, 1); after a(6) = 311 and a(7) = 411 the smallest unused term a(8) allowing the rebuilding of the sequence by multiplying its last two digits is 26 (as the product of the last two digits of 26 is 2*6 = 12); now the succession of the products is 0, 1, 1, 1, 1, 1, 1, 2 which is the succession of the sequence's digits itself); etc.
Links
- Jean-Marc Falcoz, Table of n, a(n) for n = 1..10002
Crossrefs
Cf. A335214.