[seqfan] Smallest k yielding primes of form a(n) = a(n-1) + n*k

Bob Selcoe rselcoe at entouchonline.net
Thu Nov 6 19:06:42 CET 2014


Hello Seqfans,

Let sequence K(p) start with a(1) being an odd prime (p).  Let a(n) = a(n-1) + n*k, where k is the smallest number such that a(n) is prime.

This yields two sequences, K(p) and S(p), where S(p) is the sequence of primes generated by K(p).  All K(p) and S(p) are unique.

Results for p = {3,5,7}, are: 

      n 1 2 3 4 5 6 7 8 9 10 
               
      K(3) 3 1 2 2 2 2 6 3 8 2 
      S(3) 3 5 11 19 29 41 83 107 179 199 
               
      K(5) 5 1 2 1 4 1 4 1 2 1 
      S(5) 5 7 13 17 37 43 71 79 97 107 
               
      K(7) 7 2 2 3 6 2 6 3 4 2 
      S(7) 7 11 17 29 59 71 113 137 173 193 



S(3) is (essentially) A084697.  Otherwise, I can't find any other related OEIS sequences - even when starting with a(2).

Might the first few be worth submitting?

Cheers,
Bob Selcoe


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