A004515 Generalized nim sum n + n in base 5.

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

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 A308244

Adjacent sequences: A004512 A004513 A004514 * A004516 A004517 A004518

Keyword

nonn,base,look

Author

N. J. A. Sloane

Status

approved