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
FORMULA
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 12 2024
STATUS
approved