A073736 - OEIS

%I #17 Mar 14 2015 00:33:14

%S 1,2,3,6,9,14,19,26,33,42,55,64,79,96,107,126,149,166,187,216,237,260,

%T 295,320,349,392,421,452,499,530,565,626,661,702,765,810,853,922,973,

%U 1020,1095,1152,1201,1286,1345,1398,1485,1556,1621,1712,1785,1854,1951

%N Sum of primes whose index is congruent to n (mod 3); equals the partial sums of A073737 (in which sums of three successive terms form the primes).

%C For purposes of this sequence, 1 is treated as a prime. - _Harvey P. Dale_, Jul 24 2013

%H Reinhard Zumkeller, <a href="/A073736/b073736.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = Sum_{m<=n, m=n (mod 3)} p_m, where p_m is the m-th prime; that is, a(3n+k) = p_(3n) + p_(3(n-1)) + p_(3(n-2)) + ... + p_k, for 0<=k<3, where a(0)=1 and the 0th prime is taken to be 1.

%e a(10) = p_10 + p_7 + p_4 + p_1 = 29 + 17 + 7 + 2 = 55.

%t a[0] = 1; a[-1] = 0; a[-2] = 0; p[0] = 1; p[n_?Positive] := Prime[n]; a[n_] := a[n] = p[n] - a[n-1] - a[n-2]; Table[a[n], {n, 0, 60}] // Accumulate (* _Jean-François Alcover_, Jun 25 2013 *)

%t Sort[Flatten[Accumulate/@Transpose[Partition[Join[{1},Prime[Range[61]]], 3]]]] (* _Harvey P. Dale_, Jul 24 2013 *)

%o (Haskell)

%o a073736 n = a073736_list !! n

%o a073736_list = scanl1 (+) a073737_list

%o -- _Reinhard Zumkeller_, Apr 28 2013

%Y Cf. A073737.

%K easy,nice,nonn

%O 0,2

%A _Paul D. Hanna_, Aug 07 2002