A004159 Sum of digits of n^2.
0, 1, 4, 9, 7, 7, 9, 13, 10, 9, 1, 4, 9, 16, 16, 9, 13, 19, 9, 10, 4, 9, 16, 16, 18, 13, 19, 18, 19, 13, 9, 16, 7, 18, 13, 10, 18, 19, 13, 9, 7, 16, 18, 22, 19, 9, 10, 13, 9, 7, 7, 9, 13, 19, 18, 10, 13, 18, 16, 16, 9, 13, 19, 27, 19, 13, 18, 25, 16, 18, 13, 10, 18, 19, 22, 18, 25, 25, 18, 13
Offset: 0
Examples
Trajectories under the map x -> a(x): 1 -> 1 -> 1 -> 1 -> 1 -> 1 -> 1 -> 1 -> 1 -> ... 2 -> 4 -> 7 -> 13 -> 16 -> 13 -> 16 -> 13 -> 16 -> ... 3 -> 9 -> 9 -> 9 -> 9 -> 9 -> 9 -> 9 -> 9 -> ... 4 -> 7 -> 13 -> 16 -> 13 -> 16 -> 13 -> 16 -> 13 -> ... 5 -> 7 -> 13 -> 16 -> 13 -> 16 -> 13 -> 16 -> 13 -> ... 6 -> 9 -> 9 -> 9 -> 9 -> 9 -> 9 -> 9 -> 9 -> ... 7 -> 13 -> 16 -> 13 -> 16 -> 13 -> 16 -> 13 -> 16 -> ... - _R. J. Mathar_, Jul 08 2012
Links
- Zak Seidov, Table of n, a(n) for n = 0..10000
- A. S. Besicovitch, The asymptotic distribution of the numerals in the decimal representation of the squares of the natural numbers, Mathematische Zeitschrift 39 (1934), pp. 146-156.
- H. Davenport and P. Erdős, Note on normal decimals, Canadian Journal of Mathematics 4 (1952), pp. 58-63.
- Michael Drmota, Christian Mauduit and Joël Rivat, The sum-of-digits function of polynomial sequences, J. Lond. Math. Soc. (2) 84(2011), no. 1, 81--102. MR2819691 (2012f:11193)
- Bernt Lindström, On the binary digits of a power, Journal of Number Theory, Volume 65, Issue 2, August 1997, Pages 321-324.
- Christian Mauduit and Joël Rivat, La somme des chiffres des carrés, Acta Mathem. 203 (1) (2009) 107-148. MR2545827 (2010j:11119).
- H. I. Okagbue, M. O. Adamu, S. A. Iyase and A. A. Opanuga, Sequence of Integers Generated by Summing the Digits of their Squares, Indian Journal of Science and Technology, Vol 8(15), DOI: 10.17485/ijst/2015/v8i15/69912, July 2015.
- K. B. Stolarsky, The binary digits of a power, Proc. Amer. Math. Soc. 71 (1978), 1-5.
Crossrefs
Programs
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Haskell
a004159 = a007953 . a000290 -- Reinhard Zumkeller, Apr 12 2014
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Maple
read("transforms"): A004159 := proc(n) digsum(n^2) ; end proc: # R. J. Mathar, Jul 08 2012 -
Mathematica
a004159[n_Integer] := Apply[Plus, IntegerDigits[n^2]]; Table[ a004159[n], {n, 0, 100}] (* Michael De Vlieger, Jul 21 2014 *) Total[IntegerDigits[#]]&/@(Range[0,100]^2) (* Harvey P. Dale, Feb 03 2019 *) -
PARI
A004159(n)=sumdigits(n^2) \\ M. F. Hasler, Sep 23 2014
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Python
def A004159(n): return sum(int(d) for d in str(n*n)) # Chai Wah Wu, Sep 03 2014
Formula
a(10n) = a(n). If n > 1 is not a multiple of 10, then a(n)=4 iff n = 10^k+1 = A062397(k), a(n)=7 iff n is in A215614={4, 5, 32, 49, 149, 1049}, and else a(n) >= 9. - M. F. Hasler, Sep 23 2014
Comments