A339822 - OEIS

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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

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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); };