id:A091591 - OEIS Search Results

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Number of pairs of twin primes between n^2 and (n+1)^2.

+0
4

1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 2, 1, 2, 2, 1, 1, 0, 2, 1, 1, 1, 2, 2, 0, 0, 3, 2, 0, 1, 3, 2, 0, 3, 2, 1, 3, 0, 3, 2, 1, 3, 2, 4, 2, 2, 3, 0, 2, 2, 4, 0, 2, 1, 1, 5, 4, 4, 1, 2, 3, 4, 3, 5, 2, 2, 3, 2, 4, 1, 2, 2, 3, 4, 3, 0, 3, 3, 2, 4, 5, 2, 2, 3, 4, 1, 2, 3, 2, 3, 3, 1, 5, 1, 3, 4, 4, 2, 5, 3, 4, 1, 3, 5, 1, 2 (list; graph; listen)

	OFFSET	`3,8`
	COMMENT	`a(1) and a(2) are omitted because they are dependent on the treatment of the twin pair (3,5). It is conjectured that a(n)>0 for all n>122. Proving this would also prove the twin prime conjecture.` `Proving a(n)>0 for n>122 would also prove Legendre's conjecture that there is a prime between n^2 and (n+1)^2. - T. D. Noe, Feb 28 2007`
	LINKS	`T. D. Noe, Table of n, a(n) for n=3..10000` `Eric Weisstein's World of Mathematics, Twin Prime Conjecture.`
	EXAMPLE	`a(3)=1 because the interval [3^2,4^2] contains one pair of twins (11,13).` `a(9)=0 because the interval [9^2,10^2] is one of the few known intervals (given in A091592) not containing twin primes.`
	CROSSREFS	`Cf. A000290, A001359, A006512, A091592.` `Cf. A014085 (number of primes between n^2 and (n+1)^2)` `Sequence in context: A080121 A122901 A001917 this_sequence A109374 A079706 A078703` `Adjacent sequences: A091588 A091589 A091590 this_sequence A091592 A091593 A091594`
	KEYWORD	`easy,nonn,nice`
	AUTHOR	`Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 22 2004`

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.

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