A253585 Numbers whose binary expansion equals the first n digits of the binary sequence A252488 whose run lengths are given by A001511 (the ruler function).

1, 2, 4, 9, 18, 36, 72, 145, 290, 580, 1161, 2322, 4644, 9288, 18576, 37153, 74306, 148612, 297225, 594450, 1188900, 2377800, 4755601, 9511202, 19022404, 38044809, 76089618, 152179236, 304358472, 608716944, 1217433888, 2434867777, 4869735554, 9739471108

Offset

1,2

Comments

The binary sequence with run lengths given by A001511 (1,2,1,3,1,2,1,4,1, ...) begins 1001000100100001.... Truncated to the first n digits and expressed as decimal numbers, this yields:

1 1

10 2

100 4

1001 9

10010 18

100100 36

1001000 72

10010001 145

100100010 290

1001000100 580

10010001001 1161

100100010010 2322

1001000100100 4644

10010001001000 9288

100100010010000 18576

1001000100100001 37153

This is a superincreasing sequence (every element of the sequence is greater than the sum of all previous elements in the sequence).

The binary sequence appears to match the parity of A170849.

Links

Jeremy Gardiner, Table of n, a(n) for n = 1..40

Prog

(PARI) a001511(n) = valuation(n, 2) + 1;
lista(nn) = {a = 0; for (n=1, nn, for (j=1, a001511(n), a *= 2; if (n % 2, a += 1); print1(a, ", "); ); ); } \\ Michel Marcus, Jan 11 2015

Crossrefs

Cf. A001511, A170849, A252488.

Sequence in context: A101351 A293333 A111662 * A119027 A145139 A033138

Adjacent sequences: A253582 A253583 A253584 * A253586 A253587 A253588

Keyword

nonn,base

Author

Jeremy Gardiner, Jan 04 2015

Status

approved