A316758 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, 554219, 113488, 226679, 334558, 966611, 1222339, 2444678, 3456889, 9877631, 12255679, 11234558, 11224669, 22334489, 98876644, 88766449, 988775321, 9776554210, 112345589, 112246789, 122467891, 224678911, 223445789

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, do a circular permutation of the last integer of the sequence and extend the sequence with the result (this will erase a few zeros in some cases, as 100023850 becomes 238501).

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..3002

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 554219 (this is the circular permutation of the previous term, 955421);
etc.

Crossrefs

Cf. A316749 and A316750 (for other sets of "read and extend" rules).

Sequence in context: A335019 A337719 A289275 * A316750 A008382 A208742

Adjacent sequences: A316755 A316756 A316757 * A316759 A316760 A316761

Keyword

nonn,base

Author

Jean-Marc Falcoz and Eric Angelini, Jul 12 2018

Status

approved