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A174989 Partial sums of A003602. 0
1, 2, 4, 5, 8, 10, 14, 15, 20, 23, 29, 31, 38, 42, 50, 51, 60, 65, 75, 78, 89, 95, 107, 109, 122, 129, 143, 147, 162, 170, 186, 187, 204, 213, 231, 236, 255, 265, 285, 288, 309, 320, 342, 348, 371, 383, 407, 409, 434, 447, 473, 480, 507, 521, 549, 553, 582, 597 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Partial sums of Kimberling's paraphrases: if n = (2k-1)*2^m then a(n) = k. The subsequence of primes in this partial sum begins: 2, 5, 23, 29, 31, 89, 107, 109, 383, 409, 521.

I conjecture that infinitely many terms are prime. For n<=10^5, exactly 5115 terms are prime. For n<=10^7, there are 352704 prime terms. The largest prime for n<10^10 is at n=9999999983, a(n)=16666666618226308891. Below 10^100, n=(10^100)-345. Below 10^500, n=(10^500)-2414. - Griffin N. Macris, May 04 2016

Since (n^2+3n)/6 < a(n) < (n^2+5n+4)/6, the sum of reciprocals of this sequence converges to a value between 13/6 and 11/3, approximately 2.888. - Griffin N. Macris, May 07 2016

LINKS

Table of n, a(n) for n=1..58.

FORMULA

a(n) = Sum{i=1..n} A003602(i) = Sum_{i=1..n} (A000265(i) + 1)/2).

From Griffin N. Macris, May 04 2016 (Start)

a(0) = 0; a(n) = A000217(ceiling(n/2)) + a(floor(n/2)).

Asymptotically, a(n) ~ (n^2+3n)/6. (End)

MATHEMATICA

a[0]:=0;

a[n_]:=Ceiling[n/2](1+Ceiling[n/2])/2 + a[Floor[n/2]];

Array[a, 50] (* Griffin N. Macris, May 04 2016 *)

CROSSREFS

Cf. A003602, A003603, A101279, A117303.

Sequence in context: A186077 A018498 A002048 * A190809 A067941 A259711

Adjacent sequences:  A174986 A174987 A174988 * A174990 A174991 A174992

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Apr 03 2010

STATUS

approved

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Last modified August 8 23:02 EDT 2020. Contains 336300 sequences. (Running on oeis4.)