id:A065382 - OEIS Search Results

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Number of primes between n(n+1)/2 (exclusive) and (n+1)(n+2)/2 (inclusive).

+0
6

2, 1, 1, 2, 2, 1, 2, 3, 2, 2, 3, 3, 3, 3, 2, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 4, 5, 3, 6, 6, 7, 5, 5, 6, 4, 8, 5, 6, 6, 8, 6, 8, 5, 7, 5, 11, 4, 6, 9, 7, 8, 9, 8, 7, 7, 9, 7, 8, 7, 12, 5, 9, 9, 11, 9, 7, 7, 12, 10, 10, 9, 9, 9, 6, 11, 10, 11, 9, 12, 11, 12, 9, 10, 11, 12, 10, 13, 9, 11, 10 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`Inspired by the weaker Legendre conjecture that there should be at least one prime between n^2 and (n+1)^2.`
	LINKS	`T. D. Noe, Table of n, a(n) for n=1..1000`
	EXAMPLE	`a(10) = 2 because between 10(10+1)/2=55 and (10+1)(10+2)/2=66 there are 2 primes: 59, 61.`
	MATHEMATICA	`Table[ PrimePi[n(n + 1)/2] - PrimePi[n(n - 1)/2], {n, 2, 96}]`
	CROSSREFS	`A000217, A014085, A065383, A065384.` `Essentially the same as A066888 and A090970.` `Sequence in context: A103610 A109705 A025848 this_sequence A066888 A029313 A144001` `Adjacent sequences: A065379 A065380 A065381 this_sequence A065383 A065384 A065385`
	KEYWORD	`nonn`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 05 2001`
	EXTENSIONS	`Definition improved by Robert G. Wilson v (jpwilson(AT)southwind.net),Apr 22 2003`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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