A334829 The sum a(n) + a(n+1) is visible around the comma that follows a(n+1). See the Comments and Example sections for details.

1, 11, 23, 46, 91, 374, 6506, 8801, 53076, 18777, 18533, 73109, 16428, 95371, 117992, 133632, 516246, 4987805, 50405105, 539291005, 896961101, 4362521065, 2594821666, 9573427311, 21682489773, 12559170843, 42416606165, 49757770089, 21743762547, 15015326363, 67590889108, 26062154719, 36530438276, 25925929956

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, May 13 2020

Keywords

• base
• nonn

Comments

The rule used here is that the rightmost digit of a(n+1) is the first digit of the sum a(n) + a(n+1), the other digits of the said sum being put after the comma in order to start a(n+2).

As no digit 0 (zero) can start a term, one will have to backtrack sometimes in order to extend the sequence - and pick another term for a(n+1), compatible with the above rule. This is always possible.

Note that the sequence is not monotonically increasing as shown by a(10) and a(11) for instance; still, the 1000th term is 406-digit long.

The sequence is always extended with the smallest available integer not yet present that does not lead to a contradiction.

Examples

			a(1) + a(2) is 1 + 11 = 12 and 12 can be seen here: 1(1,2)3,
a(2) + a(3) is 11 + 23 = 34 and 34 can be seen here: 2(3,4)6,
a(3) + a(4) is 23 + 46 = 69 and 69 can be seen here: 4(6,9)1,
a(4) + a(5) is 46 + 91 = 137 and 137 can be seen here: 9(1,37)4,
a(5) + a(6) is 91 + 374 = 465 and 465 can be seen here: 37(4,65)06, etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..1002
• E. Angelini More and more commas on the SeqFan mailing list, May 12 2020.

Crossrefs

Cf. A121805, A230450, A197756.