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A237881 a(n) = 2-adic valuation of prime(n)+prime(n+1). 1
0, 3, 2, 1, 3, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 4, 3, 7, 1, 4, 3, 1, 2, 1, 1, 2, 1, 3, 1, 4, 1, 2, 2, 5, 2, 2, 6, 1, 2, 5, 3, 2, 7, 1, 2, 1, 1, 1, 3, 1, 3, 5, 2, 2, 3, 2, 2, 2, 1, 2, 6, 3, 1, 4, 1, 3, 2, 2, 3, 1, 3, 1, 2, 4, 1, 2, 1, 1, 1, 2, 3, 2, 5, 3, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 3, 6, 4, 5, 2, 2, 2, 2, 2, 3, 4, 3, 2, 1, 2, 1, 3, 2, 1, 2, 5, 3, 1, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A007814(A001043(n)).
a(n) << log n; in particular, a(n) <= log_2 n + log_2 log n + O(1). - Charles R Greathouse IV, Feb 14 2014
EXAMPLE
a(5)=3 because prime(5)=11, prime(6)=13, 11+13=24=2^3*3, 2-adic valuation(24)=3.
MATHEMATICA
IntegerExponent[ListConvolve[{1, 1}, Prime[Range[200]]], 2] (* Paolo Xausa, Nov 02 2023 *)
PROG
(PARI) {for(i=1, 200, k=valuation(prime(i)+prime(i+1), 2); print1(k, ", "))}
(Python)
from sympy import prime
def A237881(n): return (~(m:=prime(n)+prime(n+1))&m-1).bit_length() # Chai Wah Wu, Jul 08 2022
CROSSREFS
Sequence in context: A085068 A265027 A079587 * A112745 A205564 A036585
KEYWORD
nonn,easy
AUTHOR
Antonio Roldán, Feb 14 2014
STATUS
approved

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Last modified June 13 00:21 EDT 2024. Contains 373362 sequences. (Running on oeis4.)