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A172113 Partial sums of the generalized Cuban primes A007645. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
LINKS
FORMULA
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}.
EXAMPLE
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.
MAPLE
Contribution from R. J. Mathar, Apr 24 2010: (Start)
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:
A172113 := proc(n) add( A007645(i), i=1..n) ; end proc: seq(A172113(n), n=1..80) ; (End)
CROSSREFS
Sequence in context: A166119 A041403 A077126 * A172112 A227347 A068043
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 25 2010
EXTENSIONS
a(5) corrected and more terms appended by R. J. Mathar, Feb 07 2010
Edited by N. J. A. Sloane, Sep 26 2010, Jan 29 2013.
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)