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.
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:
CROSSREFS
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