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A219794 First differences of 5-smooth numbers (A051037). 1
1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 2, 4, 1, 2, 3, 2, 4, 4, 5, 3, 2, 4, 6, 4, 8, 3, 5, 1, 9, 6, 4, 8, 12, 5, 3, 7, 9, 6, 10, 2, 18, 12, 8, 16, 9, 15, 3, 7, 6, 14, 18, 12, 20, 4, 36, 15, 9, 16, 5, 27, 18, 30, 6, 14, 12, 28, 36, 24, 25, 15, 8, 27, 45, 9, 21, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

lim inf a(n) >= 2 by Størmer's theorem. Is lim a(n) = infinity? It would be very surprising if this was false, since then there is some k such that n and n+k are both 5-smooth for infinitely many n. - Charles R Greathouse IV, Nov 28 2012

A085152 gives all n's for which a(n) = 1. Thue-Siegel-Roth theorem gives lim a(n) = infinity. With the aid of lower bounds for linear forms in logarithms, Tijdeman showed that a(n+1)-a(n) > a(n)/(log a(n))^C for some effectively computable constant C. - Tomohiro Yamada, Apr 15 2017

LINKS

Zak Seidov, Table of n, a(n) for n = 1..1000

C. Stormer, Quelques théorèmes sur l'équation de Pell x^2 - Dy^2 = +-1 et leurs applications, Skrifter Videnskabs-selskabet (Christiania), Mat.-Naturv. Kl. I (2), 48 pp.

R. Tijdeman, On integers with many small prime factors, Compos. Math. 26 (1973), 319--330.

FORMULA

a(n) = A051037(n+1) - A051037(n).

CROSSREFS

Cf. A051037, A085152.

Sequence in context: A181118 A179009 A112757 * A286334 A118492 A079246

Adjacent sequences:  A219791 A219792 A219793 * A219795 A219796 A219797

KEYWORD

nonn

AUTHOR

Zak Seidov, Nov 28 2012

STATUS

approved

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Last modified September 25 15:49 EDT 2020. Contains 337344 sequences. (Running on oeis4.)