A172113 Partial sums of the generalized Cuban primes A007645.

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

Offset: 1

Author

Jonathan Vos Post, Jan 25 2010

Keywords

• easy
• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A000040, A007645, A038349.

Programs

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)

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}.

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.