A344184 - OEIS

%I #12 May 14 2021 02:57:09

%S 1,2,6,12,44,44,92,184,1208,1336,5304,5304,10680,10680,21368,42736,

%T 567024,673520,5383920,5383920,21535472,172283632,172283632,172283632,

%U 344774384,344774384,344774384,344774384,689559280,689559280,1379118576,2758237152,71477713888

%N 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.

%C This sequence is a variant of A056744, easier to compute.

%C This sequence is not weakly increasing; a(109) < a(108).

%H Rémy Sigrist, <a href="/A344184/b344184.txt">Table of n, a(n) for n = 1..1024</a>

%H Rémy Sigrist, <a href="/A344184/a344184.png">Binary plot of the first 1024 terms</a>

%H Rémy Sigrist, <a href="/A344184/a344184.gp.txt">PARI program for A344184</a>

%F A144016(a(n)) >= n.

%e The first terms, alongside their binary expansion, are:

%e   n   a(n)   bin(n)  bin(a(n))

%e   --  -----  ------  ---------------

%e    1      1       1                1

%e    2      2      10               10

%e    3      6      11              110

%e    4     12     100             1100

%e    5     44     101           101100

%e    6     44     110           101100

%e    7     92     111          1011100

%e    8    184    1000         10111000

%e    9   1208    1001      10010111000

%e   10   1336    1010      10100111000

%e   11   5304    1011    1010010111000

%e   12   5304    1100    1010010111000

%e   13  10680    1101   10100110111000

%e   14  10680    1110   10100110111000

%e   15  21368    1111  101001101111000

%o (PARI) See Links section.

%Y Cf. A056744, A144016, A344183.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, May 11 2021