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A073736 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). 3
1, 2, 3, 6, 9, 14, 19, 26, 33, 42, 55, 64, 79, 96, 107, 126, 149, 166, 187, 216, 237, 260, 295, 320, 349, 392, 421, 452, 499, 530, 565, 626, 661, 702, 765, 810, 853, 922, 973, 1020, 1095, 1152, 1201, 1286, 1345, 1398, 1485, 1556, 1621, 1712, 1785, 1854, 1951 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For purposes of this sequence, 1 is treated as a prime. - Harvey P. Dale, Jul 24 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

FORMULA

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.

EXAMPLE

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

MATHEMATICA

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-Fran├žois Alcover, Jun 25 2013 *)

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

PROG

(Haskell)

a073736 n = a073736_list !! n

a073736_list = scanl1 (+) a073737_list

-- Reinhard Zumkeller, Apr 28 2013

CROSSREFS

Cf. A073737.

Sequence in context: A074150 A261243 A061925 * A101593 A226893 A084628

Adjacent sequences:  A073733 A073734 A073735 * A073737 A073738 A073739

KEYWORD

easy,nice,nonn

AUTHOR

Paul D. Hanna, Aug 07 2002

STATUS

approved

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Last modified September 24 04:19 EDT 2020. Contains 337317 sequences. (Running on oeis4.)