A243354 Permutation of natural numbers which maps between the partitions as encoded in A112798 (prime-index based system, one-based) to A227739 (binary based system, zero-based).

0, 1, 3, 2, 7, 6, 15, 5, 4, 14, 31, 13, 63, 30, 12, 10, 127, 9, 255, 29, 28, 62, 511, 26, 8, 126, 11, 61, 1023, 25, 2047, 21, 60, 254, 24, 18, 4095, 510, 124, 58, 8191, 57, 16383, 125, 27, 1022, 32767, 53, 16, 17, 252, 253, 65535, 22, 56, 122, 508, 2046, 131071

Offset: 1

Author

Antti Karttunen, Jun 05 2014

Keywords

• nonn

Comments

Note the indexing: the domain starts from one, but the range also includes zero.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A243353.

Cf. A227739, A112798, A006068, A156552, A075158, A241909.

Programs

Scheme

(define (A243354 n) (A006068 (A156552 n)))

Formula

a(n) = A006068(A156552(n)).

a(n) = A075158(A241909(n)-1). [With A075158's original starting offset].

For all n >= 1, A243353(a(n)) = n.

A056239(n) = A227183(a(n)).

A003963(n) = A227184(a(n)).

A037481(n) = a(A002110(n)).