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 A003681 a(n) = min { p +- q : p +- q > 1 and p*q = Product_{k=1..n-1} a(k) }. (Formerly M0659) 22
 2, 3, 5, 7, 11, 13, 17, 107, 197, 3293, 74057, 1124491, 1225063003, 48403915086083, 229199690093487791653, 139394989871393443893426292667, 2310767115930351361890156080500119173238113, 521722354210765171422123515738862106081757768167379798858040637 (list; graph; refs; listen; history; text; internal format)
 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(#a1||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 Cf. A082120, A082125. Cf. A033676, A033677, A056737, A219695. Sequence in context: A053434 A241716 A061166 * A217147 A029732 A037950 Adjacent sequences:  A003678 A003679 A003680 * A003682 A003683 A003684 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

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Last modified March 31 19:37 EDT 2020. Contains 333151 sequences. (Running on oeis4.)