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.
%I A020942 #45 Mar 09 2025 12:51:20
%S A020942 1,5,7,10,14,18,20,24,26,29,33,35,38,42,46,48,51,55,59,61,65,67,70,74,
%T A020942 78,80,84,86,89,93,95,98,102,106,108,112,114,117,121,123,126,130,134,
%U A020942 136,139,143,147,149,153,155,158,162,164,167,171,175,177,180,184
%N A020942 First column of 3rd-order Zeckendorf array A136189.
%C A020942 I would like to get similar sequences where the least term in the representation is 2 [gives 2 8 11 15 21 27 30..., which is now A064105], 3, 4, 6, etc. They are the 2nd, 3rd, etc. columns of the 3rd-order Zeckendorf array. [See cross-references. - _N. J. A. Sloane_, Apr 29 2024]
%C A020942 These have now been entered in the OEIS as
%C A020942 column 1: A020942.
%C A020942 column 2: A064105.
%C A020942 column 3: A064106.
%C A020942 column 4: A372749.
%C A020942 column 5: A372750.
%C A020942 column 6: A372752.
%C A020942 column 7: A372756.
%C A020942 column 8: A372757.
%H A020942 A.H.M. Smeets, <a href="/A020942/b020942.txt">Table of n, a(n) for n = 1..20000</a>
%H A020942 Larry Ericksen and Peter G. Anderson, <a href="http://www.cs.rit.edu/~pga/k-zeck.pdf">Patterns in differences between rows in k-Zeckendorf arrays</a>, The Fibonacci Quarterly, Vol. 50, February 2012. - _N. J. A. Sloane_, Jun 10 2012
%H A020942 Clark Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/33-1/kimberling.pdf">The Zeckendorf array equals the Wythoff array</a>, Fibonacci Quarterly 33 (1995) 3-8.
%H A020942 Jeffrey Shallit, <a href="https://arxiv.org/abs/2503.01026">The Narayana Morphism and Related Words</a>, arXiv:2503.01026 [math.CO], 2025.
%F A020942 Any number n has unique representation as a sum of terms from {1, 2, 3, 4, 6, 9, 13, 19, ...} (cf. A000930) such that no two terms are adjacent or pen-adjacent; e.g., 7=6+1. Sequence gives all n where that representation involves 1.
%F A020942 Conjecture: a(n) = A202342(n) + n. - _Sean A. Irvine_, May 05 2019 [proved in corrected form in Shallit (2025); it should read a(n) = A202342(n) + n-1]
%F A020942 a(n) = A136496(n) - 1. - _Jeffrey Shallit_, Mar 08 2025
%e A020942 1=1; 5=4+1; 7=6+1; 10=9+1; etc.
%Y A020942 Cf. A000930, A064105, A064106, A136189, A136496, A202342, A372749, A372750, A372752, A372756, A372757.
%K A020942 nonn,easy,nice
%O A020942 1,2
%A A020942 _Clark Kimberling_
%E A020942 More terms from _Naohiro Nomoto_, Sep 17 2001