

A003681


a(n) = min { p + q : p + q > 1 and p*q = Product_{k=1..n1} a(k) }.
(Formerly M0659)


22



2, 3, 5, 7, 11, 13, 17, 107, 197, 3293, 74057, 1124491, 1225063003, 48403915086083, 229199690093487791653, 139394989871393443893426292667, 2310767115930351361890156080500119173238113, 521722354210765171422123515738862106081757768167379798858040637
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OFFSET

1,1


COMMENTS

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



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[#di]>1next; a=concat(a, d[i+1]d[#di]); break)); a} \\ May require allocatemem() for N >= 15.  M. F. Hasler, Aug 17 2015


CROSSREFS



KEYWORD

nonn,hard,nice


AUTHOR



EXTENSIONS



STATUS

approved



