A339822 The exponent of the highest power of 2 dividing A339821(n).

0, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 3, 4, 5, 6, 3, 4, 5, 6, 4, 5, 6, 7, 4, 5, 6, 7, 5, 6, 7, 8, 5, 6, 7, 8, 6, 7, 8, 9, 6, 7, 8, 9, 7, 8, 9, 10, 7, 8, 9, 10, 8, 9, 10, 11, 1, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 3, 4, 5, 6, 3, 4, 5, 6, 4, 5, 6, 7, 4, 5, 6, 7, 5, 6, 7, 8, 5, 6, 7, 8, 6, 7, 8, 9, 6, 7

Offset: 0

Author

Antti Karttunen, Dec 18 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000010, A003972, A007814, A019565, A023506, A053574, A339814, A339815, A339821.

Programs

PARI

A339822(n) = { my(s=0, p=2); while(n>0, p = nextprime(1+p); if(n%2, s += valuation((p-1),2)); n >>= 1); (s); };

Formula

If 4n = 2^e1 + 2^e2 + ... + 2^ek [e1 ... ek distinct], then a(n) = A023506(e1) + A023506(e2) + ... + A023506(ek).

a(n) = A007814(A339821(n)) = A053574(A019565(2n)).

a(n) = A007814(A003972(A019565(n))) = A007814(A000010(A019565(2n))).