A161754 a(n) = sum of all nonprimes from nonprime(p) to nonprime(q) where p is nonprime(n+1) and q is nonprime(n+2).

11, 23, 31, 26, 29, 49, 59, 43, 46, 75, 81, 58, 62, 99, 69, 71, 74, 77, 121, 131, 91, 94, 97, 99, 153, 106, 109, 168, 175, 122, 125, 192, 131, 134, 137, 139, 216, 149, 151, 153, 155, 239, 247, 169, 171, 173, 175, 269, 183, 185, 282, 289, 197, 199, 202, 206, 315, 214, 218

Offset

1,1

Comments

For convenience "nonprime(n)" is used for "n-th nonprime". Here the nonprimes start at 0 (see A141468), so nonprime(1) to nonprime(20) are 0, 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28.

Links

Table of n, a(n) for n=1..59.

Example

n = 1: nonprime(1+1) = 1, nonprime(1+2) = 4. Sum of all nonprimes from nonprime(1) = 0 to nonprime(4) = 6 is 0+1+4+6, hence a(1) = 11.
n = 4: nonprime(4+1) = 8, nonprime(4+2) = 9. Sum of all nonprimes from nonprime(8) = 12 to nonprime(9) = 14 is 12+14, hence a(4) = 26.
n = 11: nonprime(11+1) = 18, nonprime(11+2) = 20. Sum of all nonprimes from nonprime(18) = 26 to nonprime(20) = 28 is 26+27+28, hence a(11) = 81.

Prog

(Magma) Nonprimes:=[0] cat [ n: n in [1..120] | not IsPrime(n) ];
NthNonprime:= func< n | Nonprimes[n] >;
[ &+[ k: k in [NthNonprime(p)..NthNonprime(q)] | not IsPrime(k) ] where p is NthNonprime(n+1) where q is NthNonprime(n+2): n in [1..60] ];

Crossrefs

Cf. A114381, A141468.

Sequence in context: A259560 A136001 A158203 * A038904 A179630 A060399

Adjacent sequences: A161751 A161752 A161753 * A161755 A161756 A161757

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 18 2009

Extensions

Edited and corrected (a(47)=175 inserted) by Klaus Brockhaus, Jun 22 2009

Status

approved