id:A058188 - OEIS Search Results

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Number of primes between prime(n) and prime(n) + sqrt(prime(n)), where prime(n) is the n-th prime.

+0
2

1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 2, 1, 0, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 1, 1, 3, 4, 3, 2, 2, 1, 2, 3, 3, 4, 3, 3, 2, 1, 1, 3, 2, 1, 1, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 3, 2, 4, 3, 4, 3, 3, 4, 4, 3, 3, 2, 2, 3, 4, 3, 3, 3, 2, 2, 1, 3 (list; graph; listen)

	OFFSET	`1,12`
	COMMENT	`Conjecture: if prime(n)>=127, there is always at least one prime between prime(n) and prime(n) + sqrt(prime(n)). Easily checked for prime(n)<1.1e15 in existing maximal gap tables`
	REFERENCES	`R. K. Guy: Unsolved problems in number theory, 2nd ed., Springer-Verlag,1994; Sections A8, A 9.` `Paulo Ribenboim: The little book of big primes, Springer-Verlag,1991; 142ff`
	LINKS	`T. D. Noe, Table of n, a(n) for n = 1..10000`
	EXAMPLE	`a(12) = 2 because between p(12)= 37 and 37+sqrt(37) = 43.08 there are two primes: 41 and 43`
	CROSSREFS	`Cf. A030296.` `Sequence in context: A126389 A105551 A073772 this_sequence A070000 A037803 A030410` `Adjacent sequences: A058185 A058186 A058187 this_sequence A058189 A058190 A058191`
	KEYWORD	`nonn`
	AUTHOR	`Adam Kertesz (adamkertesz(AT)worldnet.att.net), Dec 04 2000`

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.

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