A051349 Sum of first n nonprimes.

0, 1, 5, 11, 19, 28, 38, 50, 64, 79, 95, 113, 133, 154, 176, 200, 225, 251, 278, 306, 336, 368, 401, 435, 470, 506, 544, 583, 623, 665, 709, 754, 800, 848, 897, 947, 998, 1050, 1104, 1159, 1215, 1272, 1330, 1390, 1452, 1515, 1579, 1644, 1710, 1778, 1847, 1917

Offset: 0

Author

Armand Turpel (armandt(AT)unforgettable.com)

Keywords

• nonn
• easy

Comments

Partial sums of A141468 or A018252. - R. J. Mathar, Mar 01 2009

The lexicographically earliest sequence with first differences as increasing sequence of composites A002808. Complement of A175970. See A175965, A175966, A175967, A014284, A175969, A175970. - Jaroslav Krizek, Oct 31 2010

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A014284, A018252, A122998, A141468, A175965, A175966, A175967, A175969, A175970.

Programs

Maple

ithnonprime := proc(n)local k: option remember: if(n=1)then return 1: fi: for k from procname(n-1)+1 do if(not isprime(k))then return k fi: od: end: A051349 := proc(n) option remember: local k: if(n<=1)then return n: fi: return ithnonprime(n)+procname(n-1): end: seq(A051349(n),n=0..51); # Nathaniel Johnston, May 25 2011

Mathematica

lst={};s=0;Do[If[ !PrimeQ[n], s=s+n;AppendTo[lst, s]], {n, 0, 10^2}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 14 2008 *)

Formula

Sum_{n>=1} 1/a(n) = A122998. - Amiram Eldar, Nov 17 2020