A297165 Permutation of natural numbers: a(n) = A005940(2+A156552(n)), a(0) = 1.

1, 2, 3, 4, 5, 6, 9, 10, 7, 8, 15, 14, 25, 22, 21, 12, 11, 26, 27, 34, 35, 20, 33, 38, 49, 18, 39, 16, 55, 46, 45, 58, 13, 28, 51, 30, 125, 62, 57, 44, 77, 74, 63, 82, 65, 24, 69, 86, 121, 50, 75, 52, 85, 94, 81, 42, 91, 68, 87, 106, 175, 118, 93, 40, 17, 66, 99, 122, 95, 76, 105, 134, 343, 142, 111, 36, 115, 70, 117, 146, 143, 32

Offset: 0

Author

Antti Karttunen, Jan 05 2018

Keywords

• nonn

Comments

Note the indexing: although the domain starts from 0, the range excludes zero.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000
• David Newman, et al, New sequences from old, Discussion on SeqFan-mailing list, January 2018.
• 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: A297166.

Cf. A005940, A156552.

Cf. also A297163.

Row/column 2 of A341510 (from the term 2 onward).

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), 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 };
A297165(n) = if(!n,1,A005940(2+A156552(n))); \\ Antti Karttunen, Feb 15 2021

Scheme

(define (A297165 n) (if (zero? n) 1 (A005940 (+ 2 (A156552 n)))))

Formula

a(0) = 1; for n > 1, a(n) = A005940(2+A156552(n)).