

A186927


Lesser of two consecutive 3smooth numbers having no common divisors.


4



1, 2, 3, 8, 27, 243, 2048, 524288, 129140163, 68630377364883, 36472996377170786403, 19342813113834066795298816, 706965049015104706497203195837614914543357369, 13703277223523221219433362313025801636536040755174924956117940937101787
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OFFSET

1,2


COMMENTS

a(n) = A003586(A186771(n)); A186928(n) = A003586(A186771(n) + 1).
Subsequence of A006899: all terms are either powers of 2 or of 3.
Najman improves an algorithm of Bauer & Bennett for computing the function that measures the minimal gap size f(k) in the sequence of integers at least one of whose prime factors exceeds k. This allows us to compute values of f(k) for larger k and obtain new values of f(k).  Jonathan Vos Post, Aug 18 2011


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..21
M. Bauer and M. A. Bennett, Prime factors of consecutive integers, Mathematics of Computation 77 (2008), pp. 24552459.
Charles R Greathouse IV, Illustration of n, a(n) for n = 1..33
Filip Najman, Large strings of consecutive smooth integers, Aug 18, 2011


MATHEMATICA

smoothNumbers[p_, max_] := Module[{a, aa, k, pp, iter}, k = PrimePi[p]; aa = Array[a, k]; pp = Prime[Range[k]]; iter = Table[{a[j], 0, PowerExpand @ Log[pp[[j]], max/Times @@ (Take[pp, j  1]^Take[aa, j  1])]}, {j, 1, k}]; Table[Times @@ (pp^aa), Sequence @@ iter // Evaluate] // Flatten // Sort]; sn = smoothNumbers[3, 10^100]; Reap[For[i = 1, i <= Length[sn]  1, i++, If[CoprimeQ[sn[[i]], sn[[i + 1]]], Sow[sn[[i]]]]]][[2, 1]] (* JeanFrançois Alcover, Nov 11 2016 *)


CROSSREFS

Cf. A186711.
Sequence in context: A080568 A091339 A006277 * A177010 A300484 A004106
Adjacent sequences: A186924 A186925 A186926 * A186928 A186929 A186930


KEYWORD

nonn


AUTHOR

Charles R Greathouse IV and Reinhard Zumkeller, Mar 01 2011


STATUS

approved



