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 A383350 #21 Jun 02 2025 17:59:45 %S A383350 0,2,72,72,2814120,29436120 %N A383350 a(n) is the smallest integer k such that there are k+i groups of order a(n)+i, for i=1,...,n. %C A383350 The sequence is finite. For any multiple of 32, there are more than 32 groups of that order. Thus, the sequence 1,2,...,32 can't appear in A000001, and this sequence is at most 31 terms long. %C A383350 The sequence is either 6 or 7 terms long. This can be shown by first showing every entry of A373650 is congruent to 24 mod 48. It then follows that if n is such that A000001(n+i) = i for i=1,2,3,4, then n+8 is a multiple of 16. But then A000001(n+8) >= 14, so we can't have A000001(n+i) = i for i=1,2,3,4,8. %C A383350 From a(2) onwards, each entry is a multiple of 24, but not a multiple of 48. %C A383350 a(7) > 223000000 if it exists. %C A383350 Each entry is congruent to 0, 2 or 4 modulo 5. %e A383350 a(1) = 0 since there is 1 group of order 1. %e A383350 a(2) = 2 since there is 1 group of order 3, 2 groups of order 4. %Y A383350 Cf. A373648, A373649, A373650, A381335. %K A383350 nonn,fini,more %O A383350 1,2 %A A383350 _Robin Jones_, Apr 24 2025