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User talk:Clark Kimberling

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I got a hit on this from something completely unrelated as far as I can tell. I don't know how to automate the programming, so worked in a spreadsheet. Anyway, it stemmed from the # ways a prime can be expressed in terms of lesser primes. I hope not to have made an error but so far have:

  • prime=2 1 way
  • prime=3 1 way
  • prime=5 1 way (2+3)
  • prime=7 2 ways (5+2, 3+2+2)
  • prime=11 5 ways
  • prime=13 8 ways
  • prime=17 16 ways
  • prime=19 *not computed (32?)

If you can confirm or negate, I'd appreciate it...--Bill McEachen 02:10, 12 February 2014 (UTC)

I'm not Clark, but I have to ask: how are 2 and 3 expressed in terms of lesser primes? Alonso del Arte 13:28, 12 February 2014 (UTC)
well of course I treated the 1st 2 as default "building blocks" but you are right, as when I now search for 0,0,1,2,5,8..I get the existing sequences I checked for (A168470), though didn't check past 16. Thanks !--Bill McEachen 16:00, 12 February 2014 (UTC)


There appears to be some mis-statement in the definition of A131393 because it currently says
Rule 2 ("positive before negative"): define sequences d( ) and a( ) as follows: d(1)=0, a(1)=1 and for n>=2, d(n) is the least positive integer d such that a(n-1)+d is not among a(1), a(2),...,a(n-1), or, if no such d exists...
and yet there must always be some such d. In fact the sequence as defined appears to be a(n) = n, d(n) = 1 for all n >= 2. Are you able to correct the definition? Peter J. Taylor 23:17, 22 March 2015 (UTC)
Peter, There's certainly something wrong at A131393. I'll work on it! Thanks. (Clark)
Today I tried to repair the definition. I modified a Perl program which reproduces A131388. I added a condition which, for 0 > d(k), tries the positive case iff 0 > d(k) > d(k-1). This reproduces the 72 entries in the b-file. I am going to clean-up the program and extend the definition and the b-file. The sequences A131394, A131395, A131396, A131397 also depend on this sequence. --Georg Fischer (talk) 17:41, 23 February 2018 (EST)