A165906 Sum of first n primes divided by the n-th prime, rounded up to the nearest integer.

1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 11, 11, 11, 11, 12, 13, 13, 14, 15, 14, 15, 15, 16, 16, 17, 17, 17, 18, 18, 19, 20, 20, 20, 21, 22, 22, 21, 22, 23, 23, 24, 25, 25, 25, 26, 26, 27, 27, 28, 29, 29, 28, 29, 30, 31, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35

Offset

1,2

Links

L. Manor, Table of n, a(n) for n = 1..1000

Formula

a(n) = ceiling(Sum_{j=1..n} prime(j)) / prime(n).

Example

a(4) = ceiling((2 + 3 + 5 + 7)/7) = ceiling(17/7) = 3.

Mathematica

Module[{nn=80, pr}, pr=Prime[Range[nn]]; Ceiling[#[[2]]/#[[1]]]&/@ Thread[ {pr, Accumulate[pr]}]] (* Harvey P. Dale, Jan 29 2013 *)

Prog

(PARI) a(n) = ceil(sum(k=1, n, prime(k))/prime(n)); \\ Michel Marcus, Mar 21 2018
(PARI) first(n) = my(res = vector(n), p, s, i = 0); forprime(p = 2, , s += p; i++; res[i] = ceil(s / p); if(i==n, return(res)); \\ David A. Corneth, Mar 24 2018

Crossrefs

Cf. A007504, A165907.

Sequence in context: A336348 A177357 A320297 * A165907 A104103 A194964

Adjacent sequences: A165903 A165904 A165905 * A165907 A165908 A165909

Keyword

easy,nonn

Author

Lior Manor, Sep 30 2009

Status

approved