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 A254860 Sorted integers m = (prime(n+1)^2 - prime(n)^2)/24, where prime(n) is A000040(n), with duplicates removed. 0
 1, 2, 3, 5, 7, 10, 12, 13, 15, 17, 18, 23, 25, 27, 28, 30, 32, 33, 35, 37, 38, 40, 43, 45, 47, 52, 55, 58, 62, 65, 67, 70, 72, 75, 77, 80, 85, 87, 88, 93, 95, 100, 103, 105, 107, 110, 117, 118, 120, 127, 130, 133, 135, 137, 138, 140, 143, 147 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A069482 gives the values of (prime(n+1)^2 - prime(n)^2), in order, with duplicates. For n>=3 (prime(n+1)^2 - prime(n)^2)/24 is an integer. The list here is sorted with duplicates removed to examine the nature and scope coverage over the integers of these ratios. 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. 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)). Prime factorization of a(n) indicates every prime will appear as a factor for at least one a(n) value. LINKS MATHEMATICA DeleteDuplicates[Sort[Table[(Prime[n + 1]^2 - Prime[n]^2)/24, {n, 3, 300}]]] CROSSREFS Cf. A069482, A000040. Sequence in context: A317407 A191211 A263133 * A144726 A123885 A010062 Adjacent sequences:  A254857 A254858 A254859 * A254861 A254862 A254863 KEYWORD nonn AUTHOR Richard R. Forberg, Feb 19 2015 STATUS approved

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Last modified May 28 04:36 EDT 2020. Contains 334671 sequences. (Running on oeis4.)