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A004515 Generalized nim sum n + n in base 5. 3
0, 2, 4, 1, 3, 10, 12, 14, 11, 13, 20, 22, 24, 21, 23, 5, 7, 9, 6, 8, 15, 17, 19, 16, 18, 50, 52, 54, 51, 53, 60, 62, 64, 61, 63, 70, 72, 74, 71, 73, 55, 57, 59, 56, 58, 65, 67, 69, 66, 68, 100, 102, 104, 101, 103, 110 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

I.e., double (mod 5) each digit (0->0, 1->2, 2->4, 3->1, 4->3) of the base-5 representation of n).

First 5^n terms of the sequence form a permutation s(n) of 0..5^n-1, n >= 1; the number of inversions of s(n) is 3*(25^n-5^n)/20 (i.e., 3, 90, 2325, 58500, 1464375, ...). - Gheorghe Coserea, Apr 23 2018

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 0..15625

Index entries for sequences related to Nim-sums

Index entries for sequences that are permutations of the natural numbers

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

Array[FromDigits[IntegerDigits[#, 5] /. k_ :> Mod[2 k, 5], 5] &, 56, 0] (* Michael De Vlieger, Apr 27 2018 *)

PROG

(PARI)

a(n) = my(v=[0, 2, 4, 1, 3], b=#v); fromdigits(apply(d->v[d+1], digits(n, b)), b);

vector(56, n, a(n-1)) \\ Gheorghe Coserea, Apr 23 2018

CROSSREFS

Inverse permutation: A065256.

a(n) = A065257(n+1)-1 ("Quintal Queens" permutation).

Sequence in context: A079901 A121426 A190183 * A258219 A036560 A117297

Adjacent sequences:  A004512 A004513 A004514 * A004516 A004517 A004518

KEYWORD

nonn,base,look

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 21 11:44 EST 2019. Contains 319354 sequences. (Running on oeis4.)