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A060108
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Sequence of sums based on primes = 7 mod 8.
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0
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2, 22, 40, 92, 210, 260, 442, 672, 950, 1162, 1520, 1650, 2072, 2380, 2882, 3060, 4030, 5370, 5612, 6112, 7740, 8030, 8932, 9560, 9882, 10542, 14950, 15352, 16590, 17442, 21540, 22022, 23002, 23500, 28222, 29330, 31032, 32782, 34580, 35190
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..40.
C. Popescu, Problem 10852, American Mathematical Monthly, Vol. 108 (2001), p. 171.
C. Popescu, Roy Barbara and Omran Kouba, A Sum Related to Quadratic Residues: 10852, American Mathematical Monthly, Vol. 109 (2002), p. 208.
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FORMULA
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a(n) = Sum_{k=1..(p-1)/2} floor(k^2/p+1/2) where p is n-th prime congruent to 7 mod 8 (i.e. A007522(n)).
a(n) = (A007522(n)^2 - 1)/24. See 2nd link. - Michel Marcus, Dec 12 2017
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EXAMPLE
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For n=2, p=A007522(2)=23, so a(2)=0+0+0+1+1+2+2+3+4+4+5=22.
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PROG
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(PARI) lista(nn) = {forprime(p=2, nn, if ((p % 8) == 7, print1((p^2-1)/24, ", ")); ); } \\ Michel Marcus, Dec 12 2017
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CROSSREFS
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Cf. A007522.
Sequence in context: A227534 A126913 A019593 * A221762 A154798 A080142
Adjacent sequences: A060105 A060106 A060107 * A060109 A060110 A060111
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KEYWORD
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easy,nonn
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AUTHOR
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Marc LeBrun, Feb 27 2001
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STATUS
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approved
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