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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• look

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

Crossrefs

Inverse permutation: A065256.

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

Programs

Mathematica

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

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

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.