A369042 LCM-transform of the inverse of binary Gray code (A006068).

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

Offset

1,2

Comments

Inverse of Binary Gray code, A006068, 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(A006068(n)) = A000523(n), from which it immediately follows that A006068 has the property S mentioned in the comments of A368900, and therefore this sequence is equal to A014963(A006068(n)), for n >= 1.

Links

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

Index entries for sequences related to binary expansion of n

Formula

a(n) = lcm {1..A006068(n)} / lcm {1..A006068(n-1)}.

a(n) = A014963(A006068(n)). [See comments.]

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); };
A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ From A006068
v369042 = LCMtransform(vector(up_to, i, A006068(i)));
A369042(n) = v369042[n];
A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };

Crossrefs

Cf. A006068, A014963, A368900, A369041, A369043, A369044.

Sequence in context: A317919 A255820 A318436 * A243375 A369045 A163659

Adjacent sequences: A369039 A369040 A369041 * A369043 A369044 A369045

Keyword

nonn

Author

Antti Karttunen, Jan 12 2024

Status

approved