A253585 - OEIS

%I #16 Jan 22 2015 00:47:10

%S 1,2,4,9,18,36,72,145,290,580,1161,2322,4644,9288,18576,37153,74306,

%T 148612,297225,594450,1188900,2377800,4755601,9511202,19022404,

%U 38044809,76089618,152179236,304358472,608716944,1217433888,2434867777,4869735554,9739471108

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

%C 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:

%C 1                1

%C 10               2

%C 100              4

%C 1001             9

%C 10010            18

%C 100100           36

%C 1001000          72

%C 10010001         145

%C 100100010        290

%C 1001000100       580

%C 10010001001      1161

%C 100100010010     2322

%C 1001000100100    4644

%C 10010001001000   9288

%C 100100010010000  18576

%C 1001000100100001 37153

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

%C The binary sequence appears to match the parity of A170849.

%H Jeremy Gardiner, <a href="/A253585/b253585.txt">Table of n, a(n) for n = 1..40</a>

%o (PARI) a001511(n) = valuation(n, 2) + 1;

%o 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

%Y Cf. A001511, A170849, A252488.

%K nonn,base

%O 1,2

%A _Jeremy Gardiner_, Jan 04 2015