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 A307632 #42 Dec 09 2024 04:48:20 %S A307632 3,5,47,53,1374,1386,3738,3756,6680,6704,84626,84658,89480,89522, %T A307632 91832,91880,173092,173152,192882,192950,524587,524661,865301,865385, %U A307632 876543,876641,890479,890583,904273,904383,918859,918987,1628979,1629117,1647107,1647257,1666775 %N A307632 Index of first occurrence of n-th prime in A307720. %C A307632 It follows from the definition of A307720 that if p = k-th prime, k>1 and k odd, and q = (k+1)st prime, then the first time p appears in the sequence is at the start of a subsequence (p,1) [(p-1)/2 times], p, (1,q) [(q+1)/2 times]. %C A307632 For example, the fifth prime (11) first appears in A307720 at step 1374 at the start of the subsequence 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 11, 1, 13, 1, 13, 1, 13, 1, 13, 1, 13, 1, 13, 1, 13. %C A307632 So q appears p+1 steps after p, which explains why the terms of the present sequence appear in pairs. %C A307632 In fact, it appears that one can make a much stronger statement about what happens immediately after the first occurrence of p. Look at the terms in A307720 following the first 11 at step 1374. It may be that the next O(p^2) terms are forced. %H A307632 N. J. A. Sloane, <a href="/A307632/b307632.txt">Table of n, a(n) for n = 1..1229</a> (taken from Rémy Sigrist's b-file for A307630; first 132 terms from Hans Havermann) %Y A307632 Cf. A307720, A307630, A307631. %Y A307632 First differences = A348773. %K A307632 nonn %O A307632 1,1 %A A307632 _N. J. A. Sloane_, Apr 26 2019 %E A307632 More terms from _Hans Havermann_, Apr 26 2019