OFFSET
1,1
COMMENTS
a(n) = A082120(Product_{k=1..n-1} a(k)) for n >= 3. - Robert Israel, Aug 12 2015
The + sign in the definition applies only for n = 1 and n = 2, thereafter only the - sign is relevant and will yield the minimum. The definition could be reformulated in a way similar to that of A056737. - M. F. Hasler, Aug 17 2015
REFERENCES
J. H. Conway, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Robert G. Wilson v and Sean A. Irvine, Table of n, a(n) for n = 1..19 [a(19) added by Sean A. Irvine, Jul 29 2015.]
EXAMPLE
a(4) = 7 because 2*3*5 = 30 whose divisors are 1, 2, 3, 5, 6, 10, 15 and 30. The closest p and q are 5 and 6 but its difference is 1 so the next closest p and q are 3 and 10 whose difference is 7.
MATHEMATICA
a[1] = 2; a[2] = 3; a[n_] := a[n] = Block[{d, l, t, p = Product[a[i], {i, n - 1}]}, d = Divisors[p]; l = Length[d]; t = Take[d, {l/2 - 1, l/2 + 2}]; If[t[[3]] - t[[2]] == 1, t[[4]] - t[[1]], t[[3]] - t[[2]]]]; Array[a, 16] (* Robert G. Wilson v, May 27 2012 *)
PROG
(PARI) A003681(N, a=[2, 3])={while(#a<N, my(d=divisors(prod(i=1, #a, a[i]))); for(i=(#d)\2, #d, d[i+1]-d[#d-i]>1||next; a=concat(a, d[i+1]-d[#d-i]); break)); a} \\ May require allocatemem() for N >= 15. - M. F. Hasler, Aug 17 2015
CROSSREFS
KEYWORD
nonn,hard,nice
AUTHOR
EXTENSIONS
a(15) from Robert G. Wilson v, Feb 26 1996
a(16) from Naohiro Nomoto, Jun 25 2001
a(17) from Robert G. Wilson v, Sep 15 2006
a(18) from Robert G. Wilson v, Jul 20 2009
a(19) from Sean A. Irvine, Jul 29 2015
STATUS
approved