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A079047
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Number of primes between p(n) and p(n)^2.
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0
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1, 2, 6, 11, 25, 33, 54, 64, 90, 136, 151, 207, 250, 269, 314, 393, 470, 501, 590, 655, 684, 789, 863, 976, 1138, 1226, 1267, 1353, 1394, 1493, 1846, 1944, 2108, 2156, 2454, 2511, 2692, 2877, 3004, 3201, 3395, 3470, 3825, 3901, 4044, 4118, 4580, 5058, 5225
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) counts how many new numbers we get as certain primes after the n-th step of the Eratosthenes Sieve. So I suggest the name "Eratosthenes numbers of the first kind" for this sequence. I conjecture that 25 and 64 are the only Erathostenes that are also square numbers.
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EXAMPLE
| a(1)=1 because between p(1)=2 and 2^2=4 there's one prime (3) a(3)=6 because between p(3)=5 and 5^2=25 there are 6 primes (7,11,13,17,19,23)
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PROG
| (PARI) forprime(p=2, 500, res=0; forprime(q=p+1, p^2, res=res+1); print1(res", "))
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CROSSREFS
| Cf. A055399, A066680.
Sequence in context: A084308 A067605 A072986 * A160966 A052326 A079118
Adjacent sequences: A079044 A079045 A079046 * A079048 A079049 A079050
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KEYWORD
| nonn
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AUTHOR
| Jose R. Brox (tautocrona(AT)terra.es), Feb 01 2003
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
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