[seqfan] Re: Sum of digits of primes - not divisible by 3?
njasloane at gmail.com
Sat Nov 3 03:20:35 CET 2018
Georg, A number > 3 whose digit sum is a multiple of 3 is always divisible
by 3, so cannot be prime.
But the other direction is an unsolved problem. We don't know that if we
are given k>3 and not a multiple of 3 then there is a prime with digit sum k
I did some editing to make the point clearer.
On Fri, Nov 2, 2018 at 8:20 PM Georg.Fischer <georg.fischer at t-online.de>
> Dear Sequence Fans,
> in my "coincidences" scans I just stumbled over the
> following pair:
> A001651 Numbers not divisible by 3.
> %K nonn,easy %O 1,2 %A N. J. A. Sloane
> A133223 A007605 [Sum of digits of n-th prime],
> sorted and duplicates removed. ...
> %K nonn,base %O 1,1 %A Lekraj Beedassy, Dec 19 2007
> %C Presumably this is 3 together with numbers
> greater than 1 and not divisible by 3.
> - Charles R Greathouse IV, Jul 17 2013
> This is rather astonishing to me. Has it been proven
> in the meantime? Is it contained in the paper of
> Mauduit and Rivat?
> Best regards - Georg
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