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

0,3

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to binary expansion of n

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))).

Prog

(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); };

Crossrefs

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

Sequence in context: A225926 A354761 A351064 * A194063 A194053 A194050

Adjacent sequences: A339819 A339820 A339821 * A339823 A339824 A339825

Keyword

nonn

Author

Antti Karttunen, Dec 18 2020

Status

approved