A286713 -id:A286713 - cp's OEIS frontend

A286709 For k>0, let bin(k) = the string corresponding to the binary representation of k, and neg(k) = bin(k) under the character substitution '0' <-> '1'; a(n) = the smallest positive integer not occurring earlier in the sequence such that bin(Sum_{k=1..n} a(k)) contains neg(n) as a substring.

2, 3, 4, 10, 1, 5, 7, 14, 8, 15, 11, 19, 31, 6, 24, 28, 18, 12, 50, 32, 30, 9, 21, 38, 13, 42, 63, 20, 16, 25, 64, 61, 51, 44, 27, 35, 89, 37, 87, 39, 85, 41, 83, 17, 107, 45, 79, 29, 52, 92, 75, 22, 102, 53, 71, 40, 43, 34, 23, 103, 127, 128, 62, 188, 66, 60

Offset: 1

Rémy Sigrist, May 13 2017

When considering bin(k), all leading zeros are removed: bin(2) = "10".
When considering neg(k), all leading zeros are preserved: neg(2) = "01".
The scatterplots of this sequence and of A160855 show similar entanglements of lines.
Partial sums are given by A286713.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Perl program for A286709
Rémy Sigrist, Illustration of first terms

Cf. A160855, A286713.

cp's OEIS Frontend

A286709 For k>0, let bin(k) = the string corresponding to the binary representation of k, and neg(k) = bin(k) under the character substitution '0' <-> '1'; a(n) = the smallest positive integer not occurring earlier in the sequence such that bin(Sum_{k=1..n} a(k)) contains neg(n) as a substring.

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