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Search: id:A038698
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| A038698 |
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Surfeit of 4k-1 primes over 4k+1 primes, beginning with prime 2. |
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+0
3
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| 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 3, 2, 3, 4, 5, 6, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 3, 4, 3, 4, 5, 4, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 3, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 6, 5, 6, 5, 6, 5, 6
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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a(n)<0 for infinitely many values of n - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 24 2002
First negative value is a(p(2946)) = a(26861) = -1. - David W. Wilson, Sep 27, 2002.
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REFERENCES
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Stan Wagon, The Power of Visualization, Front Range Press, 1994, p. 2.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
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FoldList[ Plus, 0, Mod[ Prime[ Range[ 2, 80 ] ], 4 ]-2 ]
a(n) = sum(k=2, n, (-1)^((prime(n)+1)/2)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 24 2002
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PROGRAM
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(PARI) for(n=2, 100, print1(sum(i=2, n, (-1)^((prime(i)+1)/2)), ", "))
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CROSSREFS
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Cf. A007350, A007351, A038691, A066520.
Cf. A112632 (race of 3k-1 and 3k+1 primes)
Cf. A156749 Another sequence showing Chebyshev bias in prime races (mod 4). [From Daniel Forgues (squid(AT)zensearch.com), Mar 26 2009]
Sequence in context: A143519 A029376 A029359 this_sequence A087991 A144095 A076092
Adjacent sequences: A038695 A038696 A038697 this_sequence A038699 A038700 A038701
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Hans Havermann (pxp(AT)rogers.com)
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