

A139043


Sum of the composite numbers <= 10^n.


0



37, 3989, 424372, 44268603, 4545653462, 462450097976, 46796680005643, 4720790259612723, 475260488407745464, 47779177572418270761, 4798532922306255318985, 481564411447949294088622
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OFFSET

1,1


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.


LINKS

Table of n, a(n) for n=1..12.


FORMULA

10^n(10^n+1)/2  1  A046731(n). Note: The bfile from Marc Deleglise was used for A046731(16) to A046731(20).


EXAMPLE

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


CROSSREFS

Cf. A046731.
Sequence in context: A231522 A030095 A334259 * A305142 A125599 A219409
Adjacent sequences: A139040 A139041 A139042 * A139044 A139045 A139046


KEYWORD

nonn


AUTHOR

Cino Hilliard, Jun 01 2008


STATUS

approved



