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A004159 Sum of digits of n^2. 49
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

H. I. Okagbue, M. O. Adamu, S. A. Iyase, 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

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, 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, Joël Rivat, La somme des chiffres des carres, Acta Mathem. 203 (1) (2009) 107-148.  MR2545827 (2010j:11119)

K. B. Stolarsky, The binary digits of a power, Proc. Amer. Math. Soc. 71 (1978), 1-5.

FORMULA

a(n)=A007953(A000290(n)); a(A058369(n))=A007953(A058369(n)). - Reinhard Zumkeller, Apr 25 2009

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

EXAMPLE

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

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 *)

PROG

(Haskell)

a004159 = a007953 . a000290  -- Reinhard Zumkeller, Apr 12 2014

(Python)

def A004159(n):

....return sum(int(d) for d in str(n*n)) # Chai Wah Wu, Sep 03 2014

(PARI) A004159(n)=sumdigits(n^2) \\ M. F. Hasler, Sep 23 2014

CROSSREFS

Cf. A007953, A159918, A056691, A268226.

Cf. A240752 (first differences), A071317 (partial sums).

Sequence in context: A296425 A056992 A169908 * A092554 A155787 A179222

Adjacent sequences:  A004156 A004157 A004158 * A004160 A004161 A004162

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 23 22:17 EST 2018. Contains 299595 sequences. (Running on oeis4.)