

A004520


Generalized nim sum n + n in base 10.


20



0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 20, 22, 24, 26, 28, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 40, 42, 44, 46, 48, 60, 62, 64, 66, 68, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 80, 82, 84, 86, 88, 0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 20, 22, 24, 26, 28, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 40, 42
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OFFSET

0,2


COMMENTS

a(n) = n + n in carryless arithmetic mod 10.  N. J. A. Sloane, Jul 23 2010.


REFERENCES

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982.
J. H. Conway, On Numbers and Games. Academic Press, NY, 1976.


LINKS

Table of n, a(n) for n=0..76.
David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version.
R. Hinze, Concrete stream calculus: An extended study, J. Funct. Progr. 20 (56) (2010) 463535, doi, Section 4.4.
Index entries for sequences related to carryless arithmetic
Index entries for sequences related to Nimsums


FORMULA

Generalized nim sum m + n in base q: write m and n in base q and add mod q with no carries, e.g. 5 + 8 in base 3 = "21" + "22" = "10" = 1.


MATHEMATICA

carrylessAdd[m_, n_, b_] := Block[{lm = IntegerLength[m, b], ln = IntegerLength[n, b]}, mx = Max[lm, ln]; idm = IntegerDigits[m, b, mx]; idn = IntegerDigits[n, b, mx]; FromDigits[ Mod[ idm + idn, b], b]]; Table[ carrylessAdd[n, n, 10], {n, 0, 76}] (* Robert G. Wilson v, Aug 23 2010 *)


PROG

(Python)
def A004520(n):
return int(''.join(str(2*int(d) % 10) for d in str(n))) # Chai Wah Wu, Jun 29 2020


CROSSREFS

When sorted and duplicates removed, gives A014263.  N. J. A. Sloane, Aug 03 2010
Sequence in context: A243590 A169933 A113603 * A169918 A169916 A073909
Adjacent sequences: A004517 A004518 A004519 * A004521 A004522 A004523


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Robert G. Wilson v, Aug 23 2010


STATUS

approved



