A297164 Permutation of nonnegative integers: a(n) = A156552(A005940(1+n)-1).

0, 1, 2, 3, 4, 7, 8, 5, 6, 17, 16, 23, 64, 65, 10, 9, 32, 19, 128, 129, 512, 67, 256, 47, 24, 4097, 20, 4099, 32768, 79, 1024, 11, 18, 31, 14, 29, 4096, 2049, 66, 515, 514, 263, 65536, 2053, 8388608, 524289, 16384, 87, 16777216, 2097153, 70, 524291, 17179869184, 287, 524288, 1037, 8388610, 289, 134217728, 1071, 520, 97, 38, 15, 12, 257, 8192, 63

Offset: 1

Author

Antti Karttunen, Jan 05 2018

Keywords

• nonn

Comments

Note the indexing: although the domain starts from 1, the range includes also zero.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..379
• Index entries for sequences related to binary expansion of n
• Index entries for sequences that are permutations of the natural numbers
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Inverse: A297163.

Cf. A005940, A156552.

Cf. also A297166, A341520, A351960.

Programs

PARI

A005940(n) = { my(p=2,t=1); n--; until(!n\=2, if(n%2, t*=p, p=nextprime(p+1))); t };
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A297164(n) = A156552(A005940(1+n)-1); \\ Antti Karttunen, Feb 27 2022

Scheme

(define (A297164 n) (A156552 (+ -1 (A005940 (+ 1 n)))))

Formula

a(n) = A156552(A005940(1+n)-1).