%I #16 Nov 30 2023 12:38:29

%S 1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,512,768,1024,1536,

%T 2048,3072,4096,6144,8192,12288,16384,24576,32768,49152,65536,98304,

%U 131072,196608,262144,341887,393216,524288,683774,786432,1048576,1572864,2097152,2495625,3145728,4194304,4991250,6291456

%N Numbers k such that A163511(k) is either k itself or its descendant in Doudna-tree, A005940 (or equally, in A163511-tree).

%C Numbers k such that A252464(k) = A364954(k), where A364954(n) is the length of the common prefix in the binary expansions of A156552(n) and A156552(A163511(n)).

%e For n = 341887, A156552(n) = 1736, "11011001000" in binary, and A163511(n) = 1830711541, with A156552(A163511(n)) = 444544, "1101100100010000000" in binary, and as the former binary expansion is a prefix of the latter, 341887 is included in this sequence. In this case, 1830711541 = A003961^7(2*341887), where A003961^7 indicates a prime shift by seven steps towards larger primes.

%e For n = 683774 = 2*341887, A156552(n) = 3473 = "110110010001", and A163511(n) = 3661423082 = 2*1830711541, with A156552(A163511(n)) = 889089, "11011001000100000001", and as the former binary expansion is a prefix of the latter, 683774 is included in this sequence.

%e For n = 1367548 = 4*341887, A156552(n) = 6947, "1101100100011" in binary, and A163511(n) = 7322846164 = 2*3661423082 with A156552(A163511(n)) = 1778179, "110110010001000000011" in binary, as the former binary expansion is NOT a prefix of the latter, 1367548 is NOT included in this sequence.

%Y Positions of 0's in A364955.

%Y Cf. A005940, A156552, A163511.

%Y Cf. A029744 (subsequence).

%Y Cf. also A364960.

%Y Cf. A252464, A364954.

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 02 2023