A161669 Sum_{j=k(n)..prime(n)} j where k is the n-th nonprime nonnegative integer.

3, 6, 9, 13, 38, 55, 108, 124, 185, 330, 376, 550, 671, 736, 897, 1155, 1470, 1566, 1927, 2178, 2266, 2664, 2958, 3444, 4158, 4521, 4653, 5037, 5215, 5580, 7182, 7656, 8418, 8602, 9999, 10251, 11128, 12040, 12597, 13566, 14570, 14875, 16683, 16951, 17612

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 16 2009, Jun 27 2009

Keywords

• nonn
• base
• easy

Examples

			n  k(n)  prime(n)  Sum_{j=k(n)..prime(n)} j
=  ====  ========  ========================
1    0       2               0 + 1 + 2 =  3 = a(1)
2    1       3               1 + 2 + 3 =  6 = a(2)
3    4       5                   4 + 5 =  9 = a(3)
4    6       7                   6 + 7 = 13 = a(4)
5    8      11         8 + 9 + 10 + 11 = 38 = a(5)
		

Programs

PARI

k=0;p=2;for(i=1,1e2,s=p*(p+1)/2-k*(k-1)/2;print1(s",");p=nextprime(p+1);while(isprime(k++),))

Extensions

Corrected and extended by Charles R Greathouse IV, Mar 25 2010

Name clarified and Example section edited by Jon E. Schoenfield, Feb 10 2019