cp's OEIS Frontend

A186927 Lesser of two consecutive 3-smooth numbers having no common divisors.

%I A186927 #23 Nov 11 2016 04:38:06
%S A186927 1,2,3,8,27,243,2048,524288,129140163,68630377364883,
%T A186927 36472996377170786403,19342813113834066795298816,
%U A186927 706965049015104706497203195837614914543357369,13703277223523221219433362313025801636536040755174924956117940937101787
%N A186927 Lesser of two consecutive 3-smooth numbers having no common divisors.
%C A186927 a(n) = A003586(A186771(n)); A186928(n) = A003586(A186771(n) + 1).
%C A186927 Subsequence of A006899: all terms are either powers of 2 or of 3.
%C A186927 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
%H A186927 Charles R Greathouse IV, <a href="/A186927/b186927.txt">Table of n, a(n) for n = 1..21</a>
%H A186927 M. Bauer and M. A. Bennett, <a href="http://www.math.ubc.ca/~bennett/erdos-graham3.pdf">Prime factors of consecutive integers</a>, Mathematics of Computation 77 (2008), pp. 2455-2459.
%H A186927 Charles R Greathouse IV, <a href="/A186927/a186927.txt">Illustration of n, a(n) for n = 1..33</a>
%H A186927 Filip Najman, <a href="http://arxiv.org/abs/1108.3710">Large strings of consecutive smooth integers</a>, Aug 18, 2011
%t A186927 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]] (* _Jean-François Alcover_, Nov 11 2016 *)
%Y A186927 Cf. A186711.
%K A186927 nonn
%O A186927 1,2
%A A186927 _Charles R Greathouse IV_ and _Reinhard Zumkeller_, Mar 01 2011