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Search: id:A125616
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| A125616 |
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(Sum of the quadratic nonresidues of prime(n)) / prime(n). |
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+0
1
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| 1, 2, 3, 3, 4, 5, 7, 7, 9, 9, 10, 11, 14, 13, 16, 15, 17, 21, 18, 22, 22, 22, 24, 25, 28, 28, 27, 28, 34, 35, 34, 36, 37, 41, 39, 41, 47, 43, 47, 45, 54, 48, 49, 54, 54, 59, 59, 57, 58, 67, 60, 66, 64, 72, 67, 73, 69, 70, 72, 73, 78, 87, 78, 79, 84, 84, 89, 87, 88, 99, 96, 93, 96
(list; graph; listen)
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OFFSET
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3,2
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COMMENT
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Always an integer for primes > 3.
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REFERENCES
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D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 185.
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LINKS
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N. Hobson, Table of n, a(n) for n = 3..1000
N. Hobson, Home page (listed in lieu of email address)
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FORMULA
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a(n)=A125615(n)/prime(n).
If prime(n) = 4k+1 then a(n) = k = A076410(n).
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EXAMPLE
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The quadratic nonresidues of 7=prime(4) are 3, 5 and 6. Hence a(4)=(3+5+6)/7=2.
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PROGRAM
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(PARI) vector(73, m, p=prime(m+2); t=1; for(i=2, (p-1)/2, t+=((i^2)%p)); (p-1)/2-t/p)
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CROSSREFS
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Cf. A002143, A076409, A076410, A125613-A125618.
Adjacent sequences: A125613 A125614 A125615 this_sequence A125617 A125618 A125619
Sequence in context: A029035 A118302 A017853 this_sequence A141472 A029034 A115339
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KEYWORD
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easy,nonn
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AUTHOR
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Nick Hobson Nov 30 2006
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