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A172113
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Partial sums of the generalized Cuban primes A007645.
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2
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3, 10, 23, 42, 73, 110, 153, 214, 281, 354, 433, 530, 633, 742, 869, 1008, 1159, 1316, 1479, 1660, 1853, 2052, 2263, 2486, 2715, 2956, 3227, 3504, 3787, 4094, 4407, 4738, 5075, 5424, 5791, 6164, 6543, 6940, 7349, 7770, 8203, 8642, 9099, 9562, 10049
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OFFSET
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1,1
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COMMENTS
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Partial sums of primes of the form 3*m+1/2+-1/2. - Juri-Stepan Gerasimov, Jan 29 2010. E.g. a(1)=3*1+1/2-1/2=3, a(2)=3+3*2+1/2+1/2=10.
The primes in this sequence begin: a(1) = 3, a(3) = 23, a(5) = 73, a(9) = 281, a(11) = 433. Of these, the subset of generalized cuban primes which are partial sums of generalized cuban primes begins: 3, 73, 433.
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LINKS
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FORMULA
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a(n) = SUM[i=1..n] A007645(i) = SUM[i=1..n] {primes of the form x^2 + xy + y^2} = SUM[i=1..n] {primes of form x^2 + 3*y^2} = SUM[i=1..n] {primes == 0 or 1 mod 3}.
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EXAMPLE
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a(30) = 3 + 7 + 13 + 19 + 31 + 37 + 43 + 61 + 67 + 73 + 79 + 97 + 103 + 109 + 127 + 139 + 151 + 157 + 163 + 181 + 193 + 199 + 211 + 223 + 229 + 241 + 271 + 277 + 283 + 307 = 4094.
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MAPLE
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A007645 := proc(n) if n <= 2 then op(n, [3, 7]) ; ; else for a from procname(n-1)+2 by 2 do if isprime(a) and (a mod 3) <> 2 then return a ; end if; end do: end if; end proc:
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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a(5) corrected and more terms appended by R. J. Mathar, Feb 07 2010
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STATUS
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approved
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