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 A254860 #14 Jul 18 2025 18:35:17
%S A254860 1,2,3,5,7,10,12,13,15,17,18,23,25,27,28,30,32,33,35,37,38,40,43,45,
%T A254860 47,52,55,58,62,65,67,70,72,75,77,80,85,87,88,93,95,100,103,105,107,
%U A254860 110,117,118,120,127,130,133,135,137,138,140,143,147
%N A254860 Sorted integers m = (prime(n+1)^2 - prime(n)^2)/24, where prime(n) is A000040(n), with duplicates removed.
%C A254860 A069482 gives the values of (prime(n+1)^2 - prime(n)^2), in order, with duplicates.
%C A254860 For n>=3 (prime(n+1)^2 - prime(n)^2)/24 is an integer.
%C A254860 The list here is sorted with duplicates removed to examine the nature and scope coverage over the integers of these ratios.
%C A254860 a(n) values have increasing differences on average, and approximately fit a curve for the n-th distinct value, given by (1/3)*n*log(n) + (3/10)*n*log(log(n))^3 for the first 10,000 values.
%C A254860 The differences between adjacent a(n) values, examined over the first 100,000 values, indicates all integers are covered (i.e., for any integer k there is at least one n where k = a(n+1) - a(n)).
%C A254860 Prime factorization of a(n) indicates every prime will appear as a factor for at least one a(n) value.
%t A254860 DeleteDuplicates[Sort[Table[(Prime[n + 1]^2 - Prime[n]^2)/24, {n, 3, 300}]]]
%t A254860 Union[Differences[Prime[Range[3,300]]^2]/24] (* _Harvey P. Dale_, Jul 18 2025 *)
%Y A254860 Cf. A069482, A000040.
%K A254860 nonn
%O A254860 1,2
%A A254860 _Richard R. Forberg_, Feb 19 2015