A371093 a(n) is the 2-adic valuation of 3n+1.

0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 8, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2

Offset

0,2

Comments

When a(n) is applied to square array A257852 we obtain square array A004736, or in other words, a(n) applied to any odd number gives the index of the row where it is located in array A257852.

See further comments in A087230.

The asymptotic density of the occurrences of k = 0, 1, 2, ... is 1/2^(k+1). The asymptotic mean of this sequence is 1. - Amiram Eldar, May 28 2024

Links

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

Formula

a(n) = A007814(A016777(n)).

For all n >= 0, A067745(1+n) = A016777(n) / 2^a(n).

Mathematica

Table[IntegerExponent[3*n+1, 2], {n, 0, 105}] (* James C. McMahon, Apr 21 2024 *)

Prog

(PARI) A371093(n) = valuation(1+3*n, 2);
(Python)
def A371093(n): return ((m:=3*n) & ~(m+1)).bit_length() # Chai Wah Wu, Apr 20 2024

Crossrefs

Bisections: A000004, A087230.

Cf. A004736, A007814, A016777, A067745, A257852.

Cf. also A371092.

Sequence in context: A158612 A143782 A073430 * A053389 A354667 A202328

Adjacent sequences: A371090 A371091 A371092 * A371094 A371095 A371096

Keyword

nonn,easy

Author

Antti Karttunen, Apr 19 2024

Status

approved