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2013 | 11 | 1 | 188-195
Tytuł artykułu

On the sum of digits of some sequences of integers

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {a n}n=1∞ that for almost all n the sum of digits of a n in base b is at least c b log n, where c b is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
1
Strony
188-195
Opis fizyczny
Daty
wydano
2013-01-01
online
2012-10-24
Twórcy
autor
autor
Bibliografia
  • [1] Bender E.A., Gao Z., Asymptotic enumeration of labelled graphs with a given genus, Electron. J. Combin., 2011, 18(1), #P13
  • [2] Chapuy G., Fusy É., Giménez O., Mohar B., Noy M., Asymptotic enumeration and limit laws for graphs of fixed genus, J. Combin. Theory Ser. A, 2011, 118(3), 748–777 http://dx.doi.org/10.1016/j.jcta.2010.11.014
  • [3] Cilleruelo J., Squares in (12 + 1) … (n 2 + 1), J. Number Theory, 2008, 128(8), 2488–2491 http://dx.doi.org/10.1016/j.jnt.2007.11.001
  • [4] Evertse J.-H., Schlickewei H.P., Schmidt W.M., Linear equations in variables which lie in a multiplicative group, Ann. of Math., 2002, 155(2), 807–836 http://dx.doi.org/10.2307/3062133
  • [5] Flajolet P., Sedgewick R., Analytic Combinatorics, Cambridge University Press, Cambridge, 2009 http://dx.doi.org/10.1017/CBO9780511801655
  • [6] Giménez O., Noy M., Asymptotic enumeration and limit laws of planar grahs, J. Amer. Math. Soc., 2009, 22(2), 309–329 http://dx.doi.org/10.1090/S0894-0347-08-00624-3
  • [7] Giménez O., Noy M., Rué J., Graph classes with given 3-connected components: asymptotic enumeration and random graphs, Random Structures Algorithms (in press)
  • [8] Knopfmacher A., Luca F., Digit sums of binomial sums, J. Number Theory, 2012, 132(2), 324–331 http://dx.doi.org/10.1016/j.jnt.2011.07.004
  • [9] Luca F., Distinct digits in base b expansions of linear recurrence sequences, Quaest. Math., 2000, 23(4), 389–404 http://dx.doi.org/10.2989/16073600009485986
  • [10] Luca F., The number of non-zero digits of n!, Canad. Math. Bull., 2002, 45(1), 115–118 http://dx.doi.org/10.4153/CMB-2002-013-9
  • [11] Luca F., On the number of nonzero digits of the partition function, Arch. Math. (Basel), 2012, 98(3), 235–240 http://dx.doi.org/10.1007/s00013-011-0350-2
  • [12] Luca F., Shparlinski I.E., On the g-ary expansions of Apéry, Motzkin, Schröder and other combinatorial numbers, Ann. Comb., 2010, 14(4), 507–524 http://dx.doi.org/10.1007/s00026-011-0074-9
  • [13] Luca F., Shparlinski I.E., On the g-ary expansions of middle binomial coefficients and Catalan numbers, Rocky Mountain J. Math., 2011, 41(4), 1291–1301 http://dx.doi.org/10.1216/RMJ-2011-41-4-1291
  • [14] Stewart C.L., On the representation of an integer in two different bases, J. Reine Angew. Math., 1980, 319, 63–72
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0080-0
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