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

1,2

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.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..1002

E. Angelini on the SeqFan mailing list, May 12 2020

Example

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.

Crossrefs

Cf. A121805, A230450, A197756.

Sequence in context: A195043 A029468 A198588 * A354589 A068231 A185005

Adjacent sequences: A334826 A334827 A334828 * A334830 A334831 A334832

Keyword

base,nonn,changed

Author

Eric Angelini and Jean-Marc Falcoz, May 13 2020

Status

approved