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 A368088 #72 Jan 01 2024 08:01:47 %S A368088 1,3,9,26,82,259,817,2583,8166,25821,81650,258200,816497,2581990, %T A368088 8164966,25819890,81649659,258198890,816496582,2581988898,8164965810, %U A368088 25819888975,81649658093,258198889748,816496580928,2581988897472,8164965809278,25819888974717,81649658092773 %N A368088 Index of smallest pentagonal number with n digits. %C A368088 The digits of the odd- and even-indexed terms converge to those in the decimal expansions of sqrt(2/3) and sqrt(20/3), respectively. %F A368088 a(n) = ceiling((sqrt(24*10^(n-1) + 1) + 1)/6). %e A368088 a(4) = 26 as the 26th pentagonal number is 26*(3*26-1)/2 = 1001 which has 4 digits (while the 25th is 925 which is only 3). %t A368088 a[n_] := Ceiling[(Sqrt[24*10^(n-1) + 1] + 1)/6]; Array[a, 40] (* _Amiram Eldar_, Dec 30 2023 *) %o A368088 (PARI) a(n) = 1 + (sqrtint(24*10^(n-1)) + 1)\6 \\ _Andrew Howroyd_, Dec 30 2023 %Y A368088 Cf. A000326, A180447. %Y A368088 Cf. A068092 (for triangular numbers), A017936 (for squares). %Y A368088 Cf. A157697 (square root of 2/3), A020772 (square root of 20/3) %K A368088 nonn,easy,base %O A368088 1,2 %A A368088 _Kelvin Voskuijl_, Dec 17 2023