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

%I A341522 #22 Mar 29 2021 01:07:56
%S A341522 2,5,6,11,10,13,14,23,18,21,22,27,26,29,30,47,34,37,38,43,42,45,46,55,
%T A341522 50,53,54,59,58,61,62,95,66,69,70,75,74,77,78,87,82,85,86,91,90,93,94,
%U A341522 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
%N A341522 a(n) = A156552(3*A005940(1+n)).
%C A341522 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.
%H A341522 Antti Karttunen, <a href="/A341522/b341522.txt">Table of n, a(n) for n = 0..8192</a>
%H A341522 Christian Krause, <a href="https://github.com/ckrause/loda">LODA, an assembly language, a computational model and a tool for mining integer sequences</a>
%H A341522 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A341522 a(n) = A156552(3*A005940(1+n)).
%F A341522 From _Antti Karttunen_, Feb 23 2021: (Start)
%F A341522 a(n) = 1 + n + A086799(1+n). - [Conjectured by LODA-miner, and easily seen to be correct]
%F A341522 a(n) = 1+ 2*n + 2^A007814(1+n). - [As the above can be rewritten to this]
%F A341522 (End)
%o A341522 (PARI)
%o A341522 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A341522 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 };
%o A341522 A341522(n) = A156552(3*A005940(1+n));
%Y A341522 Row/column 2 of A341520. Permutation of A255068.
%Y A341522 Cf. A005940, A007814, A156552, A086799, A014707 (characteristic function).
%K A341522 nonn
%O A341522 0,1
%A A341522 _Antti Karttunen_, Feb 15 2021