id:A084596 - OEIS Search Results

Search: id:A084596

Displaying 1-1 of 1 results found.

page 1

a(n) is the number of times n is in sequence A014085, i.e. there are exactly a(n) cases where there are exactly n primes between m^2 and (m+1)^2 for m>=0.

+0
2

1, 0, 4, 3, 4, 4, 4, 5, 4, 7, 5, 5, 5, 7, 2, 7, 5, 6, 4, 4, 5, 10, 6, 9, 7, 5, 2, 5, 6, 6, 10, 4, 5, 11, 5, 3, 8, 3, 8, 9, 7, 10, 5, 4, 6, 8, 8, 5, 6, 10, 8, 9, 4, 4, 6, 7, 8, 7, 5, 10, 9, 9, 6, 8, 7, 7, 7, 8, 6, 3, 5, 8, 4, 8, 14, 8, 7, 9, 10, 6, 9, 6, 7, 6, 6, 8, 10, 4, 8, 7, 6, 8, 5, 14, 6, 7, 11, 7, 10, 8 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`This sequences uses a finite number of terms of A014085 to conjecture the behavior of all terms of A014085. The first 10000 terms of this sequence were computed using 120000 terms of A014085. Legendre's conjecture is equivalent to a(0) remaining 1 for all terms of A014085. [Comment reworded by T. D. Noe, Sep 04 2008]`
	REFERENCES	`P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 143.`
	LINKS	`T. D. Noe, Table of n, a(n) for n=0..10000` `Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Landau's Problems.`
	EXAMPLE	`a(14)=2 because 14 is in sequence A014085 only two times. There are 14 primes between 64^2 and 65^2 as well as between 77^2 and 78^2. These are the only cases with exactly 14 primes.`
	CROSSREFS	`Cf. A007491, A014085, A084597.` `Sequence in context: A088910 A010308 A156743 this_sequence A056641 A010652 A088752` `Adjacent sequences: A084593 A084594 A084595 this_sequence A084597 A084598 A084599`
	KEYWORD	`nonn`
	AUTHOR	`Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2003`

page 1

Search completed in 0.002 seconds

Last modified November 29 12:46 EST 2009. Contains 167659 sequences.

AT&T Labs Research