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A139043 Sum of the composite numbers <= 10^n. 0
37, 3989, 424372, 44268603, 4545653462, 462450097976, 46796680005643, 4720790259612723, 475260488407745464, 47779177572418270761, 4798532922306255318985, 481564411447949294088622 (list; graph; refs; listen; history; text; internal format)
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 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

Adjacent sequences:  A139040 A139041 A139042 * A139044 A139045 A139046

KEYWORD

nonn

AUTHOR

Cino Hilliard, Jun 01 2008

STATUS

approved

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Last modified January 18 04:57 EST 2021. Contains 340250 sequences. (Running on oeis4.)