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A172113 Partial sums of the generalized Cuban primes A007645.

%I A172113 #11 May 01 2013 21:12:47
%S A172113 3,10,23,42,73,110,153,214,281,354,433,530,633,742,869,1008,1159,1316,
%T A172113 1479,1660,1853,2052,2263,2486,2715,2956,3227,3504,3787,4094,4407,
%U A172113 4738,5075,5424,5791,6164,6543,6940,7349,7770,8203,8642,9099,9562,10049
%N A172113 Partial sums of the generalized Cuban primes A007645.
%C A172113 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.
%C A172113 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.
%F A172113 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}.
%e A172113 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.
%p A172113 Contribution from _R. J. Mathar_, Apr 24 2010: (Start)
%p A172113 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:
%p A172113 A172113 := proc(n) add( A007645(i),i=1..n) ; end proc: seq(A172113(n),n=1..80) ; (End)
%Y A172113 Cf. A000040, A007645, A038349.
%K A172113 easy,nonn
%O A172113 1,1
%A A172113 _Jonathan Vos Post_, Jan 25 2010
%E A172113 a(5) corrected and more terms appended by _R. J. Mathar_, Feb 07 2010
%E A172113 Edited by _N. J. A. Sloane_, Sep 26 2010, Jan 29 2013.