login
A139043
Sum of the composite numbers <= 10^n.
1
37, 3989, 424372, 44268603, 4545653462, 462450097976, 46796680005643, 4720790259612723, 475260488407745464, 47779177572418270761, 4798532922306255318985, 481564411447949294088622, 48300753556627220581110505, 4842410739289313059458438978, 485307601483092493601774297633
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
Amiram Eldar, Table of n, a(n) for n = 1..26 (calculated using the b-file at 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).
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
KEYWORD
nonn
AUTHOR
Cino Hilliard, Jun 01 2008
EXTENSIONS
a(13)-a(15) from Amiram Eldar, Jun 30 2024
STATUS
approved