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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
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..56.

Rémy Sigrist, Perl program for A300082

Rémy Sigrist, Scatterplot of the first difference of the first 2^17 terms

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

Cf. A160855, A300062.

Sequence in context: A047357 A003607 A087859 * A050010 A316493 A213650

Adjacent sequences:  A300079 A300080 A300081 * A300083 A300084 A300085

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist and Chai Wah Wu, Feb 24 2018

STATUS

approved

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Last modified April 21 03:06 EDT 2021. Contains 343145 sequences. (Running on oeis4.)