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A300082 a(1) = 1, a(n) = the smallest integer > a(n-1) such that Sum_{k=1..n} a(k) written in binary contains binary n as a substring. 1

%I

%S 1,3,7,8,10,15,16,20,21,37,38,40,53,65,80,82,84,96,111,129,150,172,

%T 193,201,202,203,227,228,254,258,259,289,296,316,317,327,349,371,399,

%U 425,426,432,449,453,509,513,526,548,593,594,611,642,643,644,648,649

%N a(1) = 1, a(n) = the smallest integer > a(n-1) such that Sum_{k=1..n} a(k) written in binary contains binary n as a substring.

%C This sequence is a binary variant of A300062.

%C The scatterplot of the first difference has interesting features (see Links section).

%H Rémy Sigrist, <a href="/A300082/a300082.pl.txt">Perl program for A300082</a>

%H Rémy Sigrist, <a href="/A300082/a300082.png">Scatterplot of the first difference of the first 2^17 terms</a>

%e The first terms, alongside the binary representation of Sum_{k=1..n} a(k) with the binary representation of n in brackets, are:

%e n a(n) bin(Sum_{k=1..n} a(k))

%e -- ---- ----------------------

%e 1 1 (1)

%e 2 3 (10)0

%e 3 7 10(11)

%e 4 8 (100)11

%e 5 10 11(101)

%e 6 15 10(110)0

%e 7 16 (111)100

%e 8 20 10(1000)0

%e 9 21 1(1001)01

%e 10 37 1000(1010)

%e 11 38 (1011)0000

%e 12 40 110(1100)0

%e 13 53 10000(1101)

%e 14 65 10100(1110)

%e 15 80 1100(1111)0

%e 16 82 1111(10000)

%o (Perl) See Links section.

%Y Cf. A160855, A300062.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_ and _Chai Wah Wu_, Feb 24 2018

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Last modified May 15 18:13 EDT 2021. Contains 343920 sequences. (Running on oeis4.)