cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A355889 Concatenate the exponents of the powers of 2 in A354169(k) in increasing order, for k = 1, 2, 3, ...

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%I A355889 #25 Jul 21 2022 03:05:49
%S A355889 0,1,2,3,0,1,4,5,6,2,3,7,8,9,0,4,10,1,5,11,12,13,2,6,14,3,7,15,16,17,
%T A355889 8,9,18,19,20,0,10,21,1,4,22,5,11,23,24,25,12,13,26,27,28,2,14,29,3,6,
%U A355889 30,7,15,31,32,33,16,17,34,35,36,8,18,37,9,19,38,39,40,0,20,41,10,21,42,43,44,1,22,45,4,5,46
%N A355889 Concatenate the exponents of the powers of 2 in A354169(k) in increasing order, for k = 1, 2, 3, ...
%C A355889 It is conjectured that the Hamming weight of A354169(k) is always 0, 1, or 2. This is known to be true for at least the first 2^25 terms. (The present sequence is well-defined even if the conjecture is false.)
%C A355889 So this is a far more efficient way to present A354169 than by listing the decimal expansions.
%C A355889 The terms of A354169 that are pure powers of 2 appear in order, so it is obvious how to recover A354169 from this sequence.
%C A355889 This could be regarded as a table with (presumably) two columns, and could therefore have keyword "tabf", but that is not really appropriate, since basically it consists of the nonnegative integers with some interjections.
%H A355889 Rémy Sigrist, <a href="/A355889/b355889.txt">Table of n, a(n) for n = 1..20000</a> (first 6585 terms from N. J. A. Sloane)
%H A355889 Rémy Sigrist, <a href="/A355889/a355889.txt">C++ program</a>
%e A355889 A354169 begins 0, 1, 2, 4, 8, 3, 16, 32, 64, 12, 128, ... We ignore the initial 0, and then the binary expansions are 2^0, 2^1, 2^2, 2^3, 2^0+2^1, 2^4, 2^5, 2^6, 2^2+2^3, 2^7, ..., so the present sequence begins 0, 1, 2, 3, 0, 1, 4, 5, 6, 2, 3, 7, ...
%o A355889 (C++) See Links section.
%Y A355889 Cf. A354169, A355150, A354773, A354774, A354767, A354798, A354680.
%K A355889 nonn
%O A355889 1,3
%A A355889 _Rémy Sigrist_ and _N. J. A. Sloane_, Jul 20 2022