A139043 Sum of the composite numbers <= 10^n.

37, 3989, 424372, 44268603, 4545653462, 462450097976, 46796680005643, 4720790259612723, 475260488407745464, 47779177572418270761, 4798532922306255318985, 481564411447949294088622, 48300753556627220581110505, 4842410739289313059458438978, 485307601483092493601774297633

Offset: 1

Author

Cino Hilliard, Jun 01 2008

Keywords

• nonn

Comments

Conjecture: 10^n(10^n+1)/2 - 1 -(10^n)^2/(2*log(10^n)-1) -> a(n) as n -> infinity. Here (10^n)^2/(2*log(10^n)-1) is also conjectured to -> sum of primes < 10^n and is a very good approximation for the sum of primes < 10^n. We know that k^2/(2log(k)-1) diverges as k -> infinity. So if we can prove this limit approaches the sum of the primes <= k, then this implies the sum of primes is infinite and therefore the number of primes is infinite.

Examples

			The  sum of the composite numbers <= 10^1 is 4 + 6 + 8 + 9 + 10 = 37, the first entry in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..26 (calculated using the b-file at A046731)

Crossrefs

Cf. A046731.

Formula

a(n) = 10^n(10^n+1)/2 - 1 - A046731(n). Note: The b-file from Marc Deleglise was used for A046731(16) to A046731(20).

Extensions

a(13)-a(15) from Amiram Eldar, Jun 30 2024