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 A064789 #25 Apr 24 2025 23:02:39 %S A064789 1,3,2,6,4,5,10,8,7,9,15,13,11,12,14,21,19,17,16,18,20,28,26,24,22,23, %T A064789 25,27,36,34,32,30,29,31,33,35,45,43,41,39,37,38,40,42,44,55,53,51,49, %U A064789 47,46,48,50,52,54,66,64,62,60,58,56,57,59,61,63,65,78,76,74,72,70,68 %N A064789 Inverse permutation to A057028. %H A064789 Gerhard Ramsebner, <a href="/A064789/a064789.svg">As index of Zernike polynomials</a> (animated SVG). %H A064789 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %F A064789 a(n) = k*(k+1)/2 + abs(m) + [m<=0] where k=floor((sqrt(8*n)-1)/2), m=2*(n-1)-k*(k+2) and [] is the Iverson bracket. - _Gerhard Ramsebner_, Nov 10 2024 %e A064789 If viewed as a regular triangle: %e A064789 1; %e A064789 3, 2; %e A064789 6, 4, 5; %e A064789 10, 8, 7, 9; %e A064789 15, 13, 11, 12, 14; %e A064789 21, 19, 17, 16, 18, 20; %e A064789 28, 26, 24, 22, 23, 25, 27; %e A064789 36, 34, 32, 30, 29, 31, 33, 35; %e A064789 45, 43, 41, 39, 37, 38, 40, 42, 44; %e A064789 55, 53, 51, 49, 47, 46, 48, 50, 52, 54; %e A064789 66, 64, 62, 60, 58, 56, 57, 59, 61, 63, 65; %e A064789 78, 76, 74, 72, 70, 68... %o A064789 (PARI) a(n) = my(k=floor((sqrt(8*n)-1)/2)); my(m=2*(n-1)-k*(k+2)); k*(k+1)/2+abs(m)+(m<=0); %o A064789 for(n=1, 32, print(n ", ", a(n))) \\ _Gerhard Ramsebner_, Nov 10 2024 %K A064789 easy,nonn %O A064789 1,2 %A A064789 _N. J. A. Sloane_, Oct 20 2001 %E A064789 More terms from _David Wasserman_, Aug 14 2002