A361947 - OEIS

A361947

If the rightmost nonzero digit in the base-4 expansion of n is the digit 1, then replace 2's by 3's and vice versa; if it is the digit 2, then replace 1's by 3's and vice versa; if it is the digit 3, then replace 1's by 2's and vice versa; a(0) = 0.

0, 1, 2, 3, 4, 5, 14, 11, 8, 13, 10, 7, 12, 9, 6, 15, 16, 17, 50, 35, 20, 21, 62, 43, 56, 29, 58, 39, 44, 25, 54, 47, 32, 49, 34, 19, 52, 53, 46, 27, 40, 61, 42, 23, 28, 57, 38, 31, 48, 33, 18, 51, 36, 37, 30, 59, 24, 45, 26, 55, 60, 41, 22, 63, 64, 65, 194

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OFFSET

0,3

COMMENTS

This sequence is a self-inverse permutation of the nonnegative integers.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..16384

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = A163241(n) when A065882(n) = 1.

a(n) = A048647(n) when A065882(n) = 2.

a(n) = A057300(n) when A065882(n) = 3.

a(n) = n iff n = d * A000695(k) for some d in {1, 2, 3} and some k >= 0.

EXAMPLE

For n = 539:

- the base-4 expansion of 539 is "20123",

- the rightmost nonzero digit is 3, so we replace 1's by 2's and vice versa,

- so the base-4 expansion of a(539) is "10213", and a(539) = 295.

PROG

(PARI) a(n) = { my (m = if (n, [ [0, 1, 3, 2], [0, 3, 2, 1], [0, 2, 1, 3] ][(n / 4^valuation(n, 4)) % 4], [0, 1, 2, 3])); fromdigits(apply (d -> m[1+d], digits(n, 4)), 4); }

CROSSREFS

Cf. A000695, A048647, A057300, A065882, A163241, A361945, A361946.

Sequence in context: A306294 A098552 A245447 * A037340 A199165 A202423

Adjacent sequences: A361944 A361945 A361946 * A361948 A361949 A361950

KEYWORD

nonn,look,base

AUTHOR

Rémy Sigrist, Apr 01 2023

STATUS

approved