A369041 LCM-transform of binary Gray code (A003188).

1, 3, 2, 1, 7, 5, 2, 1, 13, 1, 1, 1, 11, 3, 2, 1, 5, 3, 1, 1, 31, 29, 1, 1, 1, 23, 1, 1, 19, 17, 2, 1, 7, 1, 1, 1, 1, 53, 1, 1, 61, 1, 1, 1, 59, 1, 1, 1, 41, 43, 1, 1, 47, 1, 1, 1, 37, 1, 1, 1, 1, 1, 2, 1, 97, 1, 1, 1, 103, 101, 1, 1, 109, 1, 1, 1, 107, 1, 1, 1, 11, 1, 1, 1, 127, 5, 1, 1, 1, 1, 1, 1, 1, 113, 1, 1, 3

Offset

1,2

Comments

Binary Gray code, A003188, is a permutation related to the binary expansion of n that keeps all the numbers of range [2^k, 2^(1+k)[ in the same range, i.e., for all n >= 1, A000523(A003188(n)) = A000523(n), from which it immediately follows that A003188 has the property S mentioned in the comments of A368900, and therefore this sequence is equal to A014963(A003188(n)), for n >= 1.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Michael De Vlieger, Scatterplot of a(n), n = 1..2^16.

Index entries for sequences related to binary expansion of n

Formula

a(n) = lcm {1..A003188(n)} / lcm {1..A003188(n-1)}.

a(n) = A014963(A003188(n)). [See comments.]

Mathematica

nn = 120; a[1] = s[1] = 1; Do[s[n] = LCM[s[n - 1], BitXor[n, Floor[n/2]] ]; a[n] = s[n]/s[n - 1], {n, 2, nn}]; Array[a, nn] (* Michael De Vlieger, Mar 24 2024 *)

Prog

(PARI)
up_to = 65537; \\ Checked up to 2^17;
LCMtransform(v) = { my(len = length(v), b = vector(len), g = vector(len)); b[1] = g[1] = 1; for(n=2, len, g[n] = lcm(g[n-1], v[n]); b[n] = g[n]/g[n-1]); (b); };
A003188(n) = bitxor(n, n>>1);
v369041 = LCMtransform(vector(up_to, i, A003188(i)));
A369041(n) = v369041[n];
A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };

Crossrefs

Cf. A000523, A003188, A014963, A368900, A369042, A369043, A369044.

Sequence in context: A001355 A364855 A105531 * A129689 A115990 A350571

Adjacent sequences: A369038 A369039 A369040 * A369042 A369043 A369044

Keyword

nonn

Author

Antti Karttunen, Jan 12 2024

Status

approved