# [seqfan] Re: No. of primes with digit sum k

RGWv rgwv at rgwv.com
Tue Dec 28 14:59:18 CET 2010

?Et al,

I would be happy to submit these nice sequences along with the
Mathematica coding.

Bob.

-----Original Message-----
From: N. J. A. Sloane
Sent: Monday, December 27, 2010 9:29 PM
To: seqfan at seqfan.eu
Cc: njas at research.att.com
Subject: [seqfan] No. of primes with digit sum k

new sequences?

These can be found on the web site
http://www.bigprimes.net/sum-of-digits/
(pointed out to me by Bill M.)
but they need a small amount of work.

Look at all the primes with exactly k digits, (in the web page,
k runs from 2 through 9).

The digit sum of a k-digit prime is a number in the range 2 through 9k-1
that is not a multiple of 3, and in general all these digit sums will occur.

The sequence (for each k = 2, 3, ...) is :

a(n) = number of k-digit primes with digit sum n, where n runs through
the non-multiples of 3 in the range [2..9k-1].

For k=2 the sequence is
1 2 2 2 3 3 3 1 1 2 1

Keywords: nonn,base,fini and for small k, also full

BigPrimes.net, <a href="//http://www.bigprimes.net/sum-of-digits/">Digit
sums of primes</a>

Note that for k=4, there is no prime with digit sum 2 (1001 is not a prime),
so the count on the web page begins at 4, so here the first term in our
sequence
will be zero.

If you can help with this small project, and will submit these sequences,

Thanks

Best regards
Neil

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