A302030 a(n) = 1+A006068(A052331(n)).

1, 2, 4, 8, 16, 3, 32, 7, 64, 15, 128, 5, 256, 31, 13, 512, 1024, 63, 2048, 9, 29, 127, 4096, 6, 8192, 255, 61, 25, 16384, 14, 32768, 511, 125, 1023, 17, 57, 65536, 2047, 253, 10, 131072, 30, 262144, 121, 49, 4095, 524288, 509, 1048576, 8191, 1021, 249, 2097152, 62, 113, 26, 2045, 16383, 4194304, 12, 8388608, 32767, 33, 505, 241, 126

Offset: 1

Author

Antti Karttunen, Apr 13 2018

Keywords

• nonn

Comments

This is the inverse of A207901 if it is considered with a starting offset 1.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

One more than A302029.

Cf. A006068, A052331, A050376, A207901.

Programs

PARI

up_to_e = 8192;
v050376 = vector(up_to_e);
ispow2(n) = (n && !bitand(n,n-1));
i = 0; for(n=1,oo,if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to_e,break));
A052331(n) = { my(s=0,e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };
A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ After code in A006068
A302030(n) = (1+A006068(A052331(n)));

Formula

a(n) = 1+A302029(n) = 1+A006068(A052331(n)).