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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
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 (list; graph; refs; listen; history; text; internal format)
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 * A068231 A185005 A073024

Adjacent sequences:  A334826 A334827 A334828 * A334830 A334831 A334832

KEYWORD

base,nonn

AUTHOR

Eric Angelini and Jean-Marc Falcoz, May 13 2020

STATUS

approved

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Last modified July 27 10:44 EDT 2021. Contains 346304 sequences. (Running on oeis4.)