A344184 Lexicographically earliest sequence of positive integers such that for any n > 0, the binary expansion of a(n) contains the binary expansion of k for k = 1..n and the binary expansion of a(n+1) is obtained by replacing a possibly empty substring of the binary expansion of a(n) by the binary expansion of n+1.
1, 2, 6, 12, 44, 44, 92, 184, 1208, 1336, 5304, 5304, 10680, 10680, 21368, 42736, 567024, 673520, 5383920, 5383920, 21535472, 172283632, 172283632, 172283632, 344774384, 344774384, 344774384, 344774384, 689559280, 689559280, 1379118576, 2758237152, 71477713888
Offset: 1
Examples
The first terms, alongside their binary expansion, are: n a(n) bin(n) bin(a(n)) -- ----- ------ --------------- 1 1 1 1 2 2 10 10 3 6 11 110 4 12 100 1100 5 44 101 101100 6 44 110 101100 7 92 111 1011100 8 184 1000 10111000 9 1208 1001 10010111000 10 1336 1010 10100111000 11 5304 1011 1010010111000 12 5304 1100 1010010111000 13 10680 1101 10100110111000 14 10680 1110 10100110111000 15 21368 1111 101001101111000
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..1024
- Rémy Sigrist, Binary plot of the first 1024 terms
- Rémy Sigrist, PARI program for A344184
Programs
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PARI
See Links section.
Formula
A144016(a(n)) >= n.
Comments