On the sum of digits of some sequences of integers

Javier Cilleruelo; Florian Luca; Juanjo Rué; Ana Zumalacárregui

Open Mathematics (2013)

  • Volume: 11, Issue: 1, page 188-195
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Javier Cilleruelo, et al. "On the sum of digits of some sequences of integers." Open Mathematics 11.1 (2013): 188-195. <http://eudml.org/doc/269574>.

@article{JavierCilleruelo2013,
abstract = {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.},
author = {Javier Cilleruelo, Florian Luca, Juanjo Rué, Ana Zumalacárregui},
journal = {Open Mathematics},
keywords = {Sum of digits; Bell numbers; sum of digits},
language = {eng},
number = {1},
pages = {188-195},
title = {On the sum of digits of some sequences of integers},
url = {http://eudml.org/doc/269574},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Javier Cilleruelo
AU - Florian Luca
AU - Juanjo Rué
AU - Ana Zumalacárregui
TI - On the sum of digits of some sequences of integers
JO - Open Mathematics
PY - 2013
VL - 11
IS - 1
SP - 188
EP - 195
AB - 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.
LA - eng
KW - Sum of digits; Bell numbers; sum of digits
UR - http://eudml.org/doc/269574
ER -

References

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  1. [1] Bender E.A., Gao Z., Asymptotic enumeration of labelled graphs with a given genus, Electron. J. Combin., 2011, 18(1), #P13 Zbl1205.05013
  2. [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 Zbl1231.05179
  3. [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 Zbl1213.11057
  4. [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 Zbl1026.11038
  5. [5] Flajolet P., Sedgewick R., Analytic Combinatorics, Cambridge University Press, Cambridge, 2009 http://dx.doi.org/10.1017/CBO9780511801655 
  6. [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 Zbl1206.05019
  7. [7] Giménez O., Noy M., Rué J., Graph classes with given 3-connected components: asymptotic enumeration and random graphs, Random Structures Algorithms (in press) Zbl1269.05060
  8. [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 Zbl1261.11005
  9. [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 Zbl1030.11004
  10. [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 Zbl1043.11008
  11. [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 Zbl1333.11009
  12. [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 Zbl1233.05020
  13. [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 Zbl1221.11020
  14. [14] Stewart C.L., On the representation of an integer in two different bases, J. Reine Angew. Math., 1980, 319, 63–72 Zbl0426.10008

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