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 A218828 #28 Feb 16 2022 11:59:27 %S A218828 1,1,2,1,2,1,1,2,1,3,1,2,1,3,2,1,2,1,3,2,1,1,2,1,3,2,1,4,1,2,1,3,2,1, %T A218828 4,3,1,2,1,3,2,1,4,3,2,1,2,1,3,2,1,4,3,2,1,1,2,1,3,2,1,4,3,2,1,5,1,2, %U A218828 1,3,2,1,4,3,2,1,5,4,1,2,1,3,2,1,4,3,2,1,5,4,3,1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,2,1,3,2,1,4,3,2,1,5,4,3,2 %N A218828 Reluctant sequence of reverse reluctant sequence A004736. %C A218828 Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A. %C A218828 Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order. %C A218828 Sequence A004736 is the reverse reluctant sequence of sequence 1,2,3,... (A000027). %H A218828 Boris Putievskiy, <a href="/A218828/b218828.txt">Rows n = 1..140 of triangle, flattened</a> %H A218828 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012. %F A218828 T(n,k) = A004736(k) for every n. %F A218828 As a linear array, the sequence is a(n) = (t1^2+3*t1+4)/2-n1, where n1=n-t(t+1)/2, t1=floor[(-1+sqrt(8*n1-7))/2], t=floor[(-1+sqrt(8*n-7))/2]. %e A218828 The start of the sequence as triangle array T(n,k) is: %e A218828 1; %e A218828 1,2; %e A218828 1,2,1; %e A218828 1,2,1,3; %e A218828 1,2,1,3,2; %e A218828 1,2,1,3,2,1; %e A218828 ... %o A218828 (Python) %o A218828 t=int((math.sqrt(8*n-7) - 1)/ 2) %o A218828 n1=n-t*(t+1)/2 %o A218828 t1=int((math.sqrt(8*n1-7) - 1)/ 2) %o A218828 m=(t1*t1+3*t1+4)/2-n1 %Y A218828 Cf. A004736, A002260, A220280. %K A218828 easy,nonn,tabl %O A218828 1,3 %A A218828 _Boris Putievskiy_, Dec 15 2012