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A371093
a(n) is the 2-adic valuation of 3n+1.
11
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
FORMULA
a(n) = A007814(A016777(n)).
For all n >= 0, A067745(1+n) = A016777(n) / 2^a(n).
G.f.: Sum_{k>=1} k*x^(-1/3 + (-2)^(k + 1)/3 + 2^k)/(1 - x^(2^(k + 1))). - Miles Wilson, Sep 30 2024
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. also A371092.
Sequence in context: A158612 A143782 A073430 * A053389 A354667 A202328
KEYWORD
nonn,easy,changed
AUTHOR
Antti Karttunen, Apr 19 2024
STATUS
approved