cp's OEIS Frontend

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.

%I A300082 #8 Feb 26 2018 19:22:14
%S A300082 1,3,7,8,10,15,16,20,21,37,38,40,53,65,80,82,84,96,111,129,150,172,
%T A300082 193,201,202,203,227,228,254,258,259,289,296,316,317,327,349,371,399,
%U A300082 425,426,432,449,453,509,513,526,548,593,594,611,642,643,644,648,649
%N 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.
%C A300082 This sequence is a binary variant of A300062.
%C A300082 The scatterplot of the first difference has interesting features (see Links section).
%H A300082 Rémy Sigrist, <a href="/A300082/a300082.pl.txt">Perl program for A300082</a>
%H A300082 Rémy Sigrist, <a href="/A300082/a300082.png">Scatterplot of the first difference of the first 2^17 terms</a>
%e A300082 The first terms, alongside the binary representation of Sum_{k=1..n} a(k) with the binary representation of n in brackets, are:
%e A300082   n     a(n)      bin(Sum_{k=1..n} a(k))
%e A300082   --    ----      ----------------------
%e A300082    1       1              (1)
%e A300082    2       3            (10)0
%e A300082    3       7           10(11)
%e A300082    4       8          (100)11
%e A300082    5      10          11(101)
%e A300082    6      15         10(110)0
%e A300082    7      16         (111)100
%e A300082    8      20        10(1000)0
%e A300082    9      21        1(1001)01
%e A300082   10      37       1000(1010)
%e A300082   11      38       (1011)0000
%e A300082   12      40       110(1100)0
%e A300082   13      53      10000(1101)
%e A300082   14      65      10100(1110)
%e A300082   15      80      1100(1111)0
%e A300082   16      82      1111(10000)
%o A300082 (Perl) See Links section.
%Y A300082 Cf. A160855, A300062.
%K A300082 nonn,base
%O A300082 1,2
%A A300082 _Rémy Sigrist_ and _Chai Wah Wu_, Feb 24 2018