A341522 a(n) = A156552(3*A005940(1+n)).

2, 5, 6, 11, 10, 13, 14, 23, 18, 21, 22, 27, 26, 29, 30, 47, 34, 37, 38, 43, 42, 45, 46, 55, 50, 53, 54, 59, 58, 61, 62, 95, 66, 69, 70, 75, 74, 77, 78, 87, 82, 85, 86, 91, 90, 93, 94, 111, 98, 101, 102, 107, 106, 109, 110, 119, 114, 117, 118, 123, 122, 125, 126, 191, 130, 133, 134, 139, 138, 141, 142, 151, 146, 149

Offset: 0

Author

Antti Karttunen, Feb 15 2021

Keywords

• nonn

Comments

Because the least significant 0-bit in A156552-code of any nonzero multiple of 3 is always alone (has 1-bit immediately to its left), it follows that A255068 (= A091067(n+1) - 1) gives these same terms in the ascending order.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192
• Christian Krause, LODA, an assembly language, a computational model and a tool for mining integer sequences
• Index entries for sequences related to binary expansion of n

Crossrefs

Row/column 2 of A341520. Permutation of A255068.

Cf. A005940, A007814, A156552, A086799, A014707 (characteristic function).

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 };
A341522(n) = A156552(3*A005940(1+n));

Formula

a(n) = A156552(3*A005940(1+n)).

From Antti Karttunen, Feb 23 2021: (Start)

a(n) = 1 + n + A086799(1+n). - [Conjectured by LODA-miner, and easily seen to be correct]

a(n) = 1+ 2*n + 2^A007814(1+n). - [As the above can be rewritten to this]

(End)