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Search: id:A086155
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| 0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 5, 6, 7, 8, 7, 8, 9, 9, 10, 11, 11, 12, 11, 12, 13, 12, 13, 14, 15, 14, 15, 16, 16, 17, 18, 17, 18, 19, 19, 20, 19, 20, 21, 19, 20, 21, 22, 22, 23, 24, 24, 25, 26, 26, 27, 23, 24, 25, 25, 26, 27, 28, 28, 29, 28, 29, 30, 31, 29, 30, 30, 31, 32, 33, 32
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n)+1=1+A086154(n) provides the length of n-th row arising in table of A086153; a(n)<=n/2 holds if n>22.
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FORMULA
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a(n)=Pi[A020483(n)]-Pi[2n+A020483(n)]-1
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EXAMPLE
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n=50: d=2n=100, p=A020483[50]=3 because by definition,3 is
the least prime so that p and p+100=103 are both primes;
a(50) here, corresponds to the number of primes between
{p,p+100}={3,103} not counting borders of interval;
thus a(50)=24, size of {5,7,...,97,101}.
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MAPLE
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Table[fl=1; Do[s0=Prime[k]; s=2*n+Prime[k]; If[PrimeQ[s]&&Equal[fl, 1], Print[PrimePi[s]-k-1]; fl=0], {k, 1, 200}], {n, 1, 25}]
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CROSSREFS
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Cf. A020483, A000720, A086153.
Sequence in context: A088023 A133316 A061451 this_sequence A094606 A080595 A123579
Adjacent sequences: A086152 A086153 A086154 this_sequence A086156 A086157 A086158
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Aug 08 2003
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