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A065382
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Number of primes between n(n+1)/2 (exclusive) and (n+1)(n+2)/2 (inclusive).
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6
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Inspired by the weaker Legendre conjecture that there should be at least one prime between n^2 and (n+1)^2.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
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EXAMPLE
| a(10) = 2 because between 10*(10+1)/2=55 and (10+1)*(10+2)/2=66 there are 2 primes: 59, 61.
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MATHEMATICA
| Table[ PrimePi[n(n + 1)/2] - PrimePi[n(n - 1)/2], {n, 2, 96}]
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CROSSREFS
| A000217, A014085, A065383, A065384.
Essentially the same as A066888 and A090970.
Sequence in context: A103610 A109705 A025848 * A066888 A029313 A144001
Adjacent sequences: A065379 A065380 A065381 * A065383 A065384 A065385
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 05 2001
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EXTENSIONS
| Definition improved by Robert G. Wilson v (jpwilson(AT)southwind.net),Apr 22 2003
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