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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
Sequence in context: A191211 A263133 A346592 * A144726 A123885 A010062
KEYWORD
nonn
AUTHOR
Richard R. Forberg, Feb 19 2015
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)