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, 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

Offset: 1

Author

Rémy Sigrist and Chai Wah Wu, Feb 24 2018

Keywords

• nonn
• base

Comments

This sequence is a binary variant of A300062.

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

Examples

			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)
		

Links

• Rémy Sigrist, Perl program for A300082
• Rémy Sigrist, Scatterplot of the first difference of the first 2^17 terms

Crossrefs

Cf. A160855, A300062.

Programs

Perl

See Links section.