A335426 a(1) = 0; thereafter a(2^(2^k)) = 0 for k > 0, and for other even numbers n, a(n) = 1+a(n/2), and for odd numbers n, a(n) = 2*a(A064989(n)).

0, 1, 2, 0, 4, 3, 8, 1, 0, 5, 16, 4, 32, 9, 6, 0, 64, 1, 128, 6, 10, 17, 256, 5, 0, 33, 2, 10, 512, 7, 1024, 1, 18, 65, 12, 2, 2048, 129, 34, 7, 4096, 11, 8192, 18, 8, 257, 16384, 6, 0, 1, 66, 34, 32768, 3, 20, 11, 130, 513, 65536, 8, 131072, 1025, 12, 2, 36, 19, 262144, 66, 258, 13, 524288, 3, 1048576, 2049, 2, 130, 24, 35, 2097152, 8, 0, 4097

Offset: 1

Author

Antti Karttunen, Jun 15 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A001146, A003961, A048675, A064989, A209229, A225546, A248663, A335427, A335428.

Cf. A082522 (gives indices of zeros after a(1)=0).

Programs

PARI

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A209229(n) = (n && !bitand(n,n-1));
A335426(n) = if(n<=2,n-1, if(!(n%2),if(A209229(n) && A209229(valuation(n,2)),0,1+A335426(n/2)), 2*A335426(A064989(n))));
\\ Alternatively:
A335426(n) = if(1==n,0, my(e=isprimepower(n)); if(e>1 && A209229(e), 0, if(!(n%2),1+A335426(n/2), 2*A335426(A064989(n)))));

Formula

a(1) = 0, and then after, a(2^(2^k)) = 0 for k > 0, and for other even numbers n, a(n) = 1+a(n/2), and for odd numbers n, a(n) = 2*a(A064989(n)).

a(n) = A335427(A225546(n)).

a(A003961(n)) = 2 * a(n).