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 A216209 #43 Nov 01 2021 04:55:37 %S A216209 0,1,2,3,2,3,4,5,6,3,4,5,6,7,8,9,4,5,6,7,8,9,10,11,12,5,6,7,8,9,10,11, %T A216209 12,13,14,15,6,7,8,9,10,11,12,13,14,15,16,17,18,7,8,9,10,11,12,13,14, %U A216209 15,16,17,18,19,20,21 %N A216209 Triangle read by rows: T(n,k) = n+k with 0 <= k <= 2*n. %C A216209 The left half together with the central column is the A051162 triangle. %C A216209 Row sums of the reciprocals of the terms in the above triangle converge to log(3). See link to Eric Naslund's answer. [_Mats Granvik_, Apr 07 2013] %C A216209 The first time that the numbers of the triplet 3k+1, 3k+2, 3k+3 appear in the sequence is for a(k^2+4*k+1) = 3*k+1, a(k^2+4*k+2) = 3*k+2, a(k^2+4*k+3) = 3*k+3 for k >= 0. - _Bernard Schott_, Jun 09 2019 %H A216209 Eric Naslund, <a href="http://math.stackexchange.com/questions/46713/euler-mascheroni-constant-expression-further-simplification/46718#46718">Euler-Mascheroni constant expression, further simplification</a> %F A216209 a(n) = floor(sqrt(n)) - floor(sqrt(n))^2 + n. - _Ridouane Oudra_, Jun 08 2019 %e A216209 Triangle begins: %e A216209 0 %e A216209 1 2 3 %e A216209 2 3 4 5 6 %e A216209 3 4 5 6 7 8 9 %e A216209 4 5 6 7 8 9 10 11 12 %e A216209 5 6 7 8 9 10 11 12 13 14 15 %e A216209 6 7 8 9 10 11 12 13 14 15 16 17 18 %e A216209 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 %p A216209 seq(seq(n+k, k=0..2*n), n=0..12); # _Ridouane Oudra_, Jun 08 2019 %Y A216209 Cf. A051162, A094727. %K A216209 nonn,tabf,easy %O A216209 0,3 %A A216209 _Alex Ratushnyak_, Mar 12 2013