A316750 A self-"read and extend" sequence built following the rules visible in the Comments section.

1, 2, 4, 8, 16, 32, 46, 92, 841, 1268, 2356, 1247, 9442, 14888, 97762, 955421, 1910842, 1234688, 2346679, 3345689, 9876631, 12235679, 12344578, 12456689, 98743321, 124466789, 233457889, 145667789, 123355789, 877654211, 1755308422, 8665443110, 88763322100, 1224456677, 1233444589, 2466889178

Offset

1,2

Comments

Start with a(1) = 1 and a(2) = 2; read the sequence digit by digit starting from the left:

when the read digit is smaller than the next one, double the last integer of the sequence and extend the sequence with the result rearranged (smallest digits first and leading zeros erased);

when the read digit is bigger than the next one, double the last integer of the sequence and extend the sequence with the result rearranged (biggest digits first, zeros at the end);

when both digits are equal, double the last integer of the sequence and extend the sequence with the simple result (no rearrangement).

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10002

Example

As the only digit of a(1) = 1 is smaller than 2 (the next digit), we extend the sequence with 4 (that is 2 times 2);
as the only digit of a(2) = 2 is smaller than 4 (the next digit), we extend the sequence with 8 (that is 2 times 4);
as the only digit of a(3) = 4 is smaller than 8 (the next digit), we extend the sequence with 16 (that is 2 times 8 -- with 1 coming before 6);
as the only digit of a(4) = 8 is bigger than 1 (the next digit), we extend the sequence with 32 (that is 2 times 16 -- with 3 coming before 2);
as the first digit of a(5) = 1 is smaller than 6 (the next digit), we extend the sequence with 46 (that is 2 times 32 = 64 that is rearranged in 46);
as the last digit of a(5) = 6 is bigger than 3 (the next digit), we extend the sequence with 92 (that is 2 times 46 = 92 rearranged in 29);
. . .
as the last digit of a(9) = 1 is equal to 1 (the next digit), we extend the sequence with 1910842 (this is simply 2 times 955421, with no rearrangement);
etc.

Crossrefs

Cf. A316749 (for another set of "read and extend" rules).

Sequence in context: A337719 A289275 A316758 * A008382 A208742 A323395

Adjacent sequences: A316747 A316748 A316749 * A316751 A316752 A316753

Keyword

base,nonn

Author

Jean-Marc Falcoz and Eric Angelini, Jul 12 2018

Status

approved