

A300082


a(1) = 1, a(n) = the smallest integer > a(n1) such that Sum_{k=1..n} a(k) written in binary contains binary n as a substring.


1



1, 3, 7, 8, 10, 15, 16, 20, 21, 37, 38, 40, 53, 65, 80, 82, 84, 96, 111, 129, 150, 172, 193, 201, 202, 203, 227, 228, 254, 258, 259, 289, 296, 316, 317, 327, 349, 371, 399, 425, 426, 432, 449, 453, 509, 513, 526, 548, 593, 594, 611, 642, 643, 644, 648, 649
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OFFSET

1,2


COMMENTS

This sequence is a binary variant of A300062.
The scatterplot of the first difference has interesting features (see Links section).


LINKS



EXAMPLE

The first terms, alongside the binary representation of Sum_{k=1..n} a(k) with the binary representation of n in brackets, are:
n a(n) bin(Sum_{k=1..n} a(k))
  
1 1 (1)
2 3 (10)0
3 7 10(11)
4 8 (100)11
5 10 11(101)
6 15 10(110)0
7 16 (111)100
8 20 10(1000)0
9 21 1(1001)01
10 37 1000(1010)
11 38 (1011)0000
12 40 110(1100)0
13 53 10000(1101)
14 65 10100(1110)
15 80 1100(1111)0
16 82 1111(10000)


PROG

(Perl) See Links section.


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



