A247891 - OEIS

A247891

a(n) is Gray-coded in base 4 into n.

0, 1, 2, 3, 5, 6, 7, 4, 10, 11, 8, 9, 15, 12, 13, 14, 21, 22, 23, 20, 26, 27, 24, 25, 31, 28, 29, 30, 16, 17, 18, 19, 42, 43, 40, 41, 47, 44, 45, 46, 32, 33, 34, 35, 37, 38, 39, 36, 63, 60, 61, 62, 48, 49, 50, 51, 53, 54, 55, 52, 58, 59, 56, 57, 85, 86, 87, 84, 90

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OFFSET

0,3

COMMENTS

Permutation of nonnegative numbers.

LINKS

Table of n, a(n) for n=0..68.

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = n XOR4 [n/4] XOR4 [n/16] XOR4 [n/64] ... XOR4 [n/4^m] where m = [log(n)/log(4)], [x] is integer floor of x, and XOR4 is a base 4 analog of binary exclusive-OR operator.

PROG

(Python)

def basexor(a, b, base):

result = 0

digit = 1

while a or b:

da = a % base

db = b % base

a //= base

b //= base

sum = (da+db) % base

result += sum * digit

digit *= base

return result

base = 4 # 2 => A006068, 3 => A105529, 10 => A226134

for n in range(129):

a = n

b = n//base

while b:

a = basexor(a, b, base)

b //= base

print str(a)+', ',

CROSSREFS

Cf. A006068 (base 2), A105529 (base 3), A226134 (base 10).

Sequence in context: A339949 A160100 A371257 * A367407 A354370 A113821

Adjacent sequences: A247888 A247889 A247890 * A247892 A247893 A247894

KEYWORD

nonn,base

AUTHOR

Alex Ratushnyak, Sep 26 2014

STATUS

approved