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 A057061 #22 Feb 24 2023 07:16:01 %S A057061 2,1,2,4,5,3,5,3,6,8,6,9,5,3,9,3,8,6,12,8,6,13,9,3,9,5,3,14,12,8,10,6, %T A057061 17,15,5,3,15,9,5,18,12,10,20,18,14,12,21,9,5,3,21,15,13,3,20,14,8,6, %U A057061 24,20,18,8,19,15,13,9,21,15,5,3,26,20,12,6 %N A057061 a(n) = number of the column of (R(i,j)) that contains prime(n), where R(i,j) is the rectangle with antidiagonals 1; 2,3; 4,5,6; ... %C A057061 The rectangle R(i,j) has this corner: %C A057061 1, 2, 4, 7, 11, 16, 22, 29, ... %C A057061 3, 5, 8, 12, 17, 23, 30, 38, ... %C A057061 6, 9, 13, 18, 24, 31, 39, 48, ... %C A057061 10, 14, 19, 25, 32, 40, 49, 59, ... %C A057061 15, 20, 26, 33, 41, 50, 60, 71, ... %C A057061 21, 27, 34, 42, 51, 61, 72, 84, ... %C A057061 28, 35, 43, 52, 62, 73, 85, 98, ... %F A057061 a(n) = A004736(prime(n)). - _Michel Marcus_, Feb 24 2023 %e A057061 The 8th prime, 19, is in column 3, so a(8) = 3. %o A057061 (PARI) f(n) = 1 + binomial(1 + floor(1/2 + sqrt(2*n)), 2) - n; \\ A004736 %o A057061 a(n) = f(prime(n)); \\ _Michel Marcus_, Feb 24 2023 %Y A057061 Cf. A000027, A000040, A004736, A185787. %Y A057061 See A057060 for primes in rows. %K A057061 nonn %O A057061 1,1 %A A057061 _Clark Kimberling_, Jul 30 2000 %E A057061 Edited by _Clark Kimberling_, Feb 12 2013