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A066339
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Number of primes p of the form 4m+1 with p <= n.
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4
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0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,13
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COMMENTS
| Asymptotic expansion: a(n) ~ pi(n)/2 ~ n/(2log(n)) (pi(n) is in sequence A000720).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
R. Breusch, An Asymptotic Formula for Primes Of The Form 4n+1
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MATHEMATICA
| Table[ Length[ Select[ Union[ Table[ Prime[ PrimePi[i]], {i, 2, n}]], Mod[ #, 4] == 1 & ]], {n, 2, 100} ]
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PROG
| (PARI) for(n=1, 200, print1(sum(i=1, n, if((i*isprime(i)-1)%4, 0, 1)), ", "))
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CROSSREFS
| Cf. A000720.
Sequence in context: A084558 A163291 A156875 * A052375 A171626 A074279
Adjacent sequences: A066336 A066337 A066338 * A066340 A066341 A066342
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KEYWORD
| nonn
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AUTHOR
| Sharon Sela (sharonsela(AT)hotmail.com), Jan 01 2002
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 03 2002
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