A110565 Results from a change in the rules leading to sequence A097357.

1, 3, 4, 14, 21, 53, 69, 237, 321, 867, 1044, 3638, 5441, 13667, 17684, 60854, 81921, 221187, 266244, 931854, 1397781, 3495477, 4542789, 15555437, 21053441

Offset

1,2

Comments

Let b_n(i) be defined as for sequence A097357. Then A097357(n) = Sum_{i>=0} b_n(i) = Sum_{i=1..n} b_n(i). We have:

Stage 1: (1,0,0,0,0,0,0,0,0,0,0,0,0) = b_1 (disregarding initial 0);

Stage 2: (1,1,0,0,0,0,0,0,0,0,0,0,0) = b_2 (disregarding initial 0);

Stage 3: (0,0,1,0,0,0,0,0,0,0,0,0,0) = b_3 (disregarding initial 0);

Stage 4: (0,1,1,1,0,0,0,0,0,0,0,0,0) = b_4 (disregarding initial 0);

Stage 5: (1,0,1,0,1,0,0,0,0,0,0,0,0) = b_5 (disregarding initial 0);

Stage 6: (1,0,1,0,1,1,0,0,0,0,0,0,0)

Stage 7: (1,0,1,0,0,0,1,0,0,0,0,0,0)

Stage 8: (1,0,1,1,0,1,1,1,0,0,0,0,0)

a(n) is defined as the number which results from interpreting the sequence b_n as a binary string read backwards from the first nonzero term.

Links

Table of n, a(n) for n=1..25.

Example

a(6) = 53 since b_6 = (1,0,1,0,1,1,0,0,0,0,0,0,0) and 110101 written in base 10 is 53.

Crossrefs

Cf. A097357.

Sequence in context: A025107 A047182 A080878 * A332270 A057433 A006074

Adjacent sequences: A110562 A110563 A110564 * A110566 A110567 A110568

Keyword

nonn,more

Author

Creighton Dement, Sep 12 2005

Status

approved