A302029 Inverse permutation of A207901: a(n) = A006068(A052331(n)).

0, 1, 3, 7, 15, 2, 31, 6, 63, 14, 127, 4, 255, 30, 12, 511, 1023, 62, 2047, 8, 28, 126, 4095, 5, 8191, 254, 60, 24, 16383, 13, 32767, 510, 124, 1022, 16, 56, 65535, 2046, 252, 9, 131071, 29, 262143, 120, 48, 4094, 524287, 508, 1048575, 8190, 1020, 248, 2097151, 61, 112, 25, 2044, 16382, 4194303, 11, 8388607, 32766, 32

Offset: 1

Author

Antti Karttunen, Apr 13 2018

Keywords

• nonn

Links

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

Crossrefs

Inverse of A207901.

One less than A302030.

Programs

PARI

up_to = 4096;
v050376 = vector(up_to);
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,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); } \\ From A006068
A302029(n) = A006068(A052331(n));

Formula

a(n) = A006068(A052331(n)).