|
|
A023528
|
|
Exponent of 2 in prime factorization of prime(n)*prime(n-1) + 1.
|
|
1
|
|
|
0, 0, 4, 2, 1, 4, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 3, 4, 3, 1, 6, 3, 1, 2, 1, 1, 2, 1, 4, 1, 4, 1, 2, 2, 3, 2, 2, 3, 1, 2, 3, 4, 2, 12, 1, 2, 1, 1, 1, 4, 1, 3, 8, 2, 2, 3, 2, 2, 2, 1, 2, 3, 5, 1, 6, 1, 5, 2, 2, 4, 1, 3, 1, 2, 3, 1, 2, 1, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Assumes the not generally accepted convention prime(0) = 1. - Michel Marcus, Jun 06 2019
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
Join[{0}, FactorInteger[#][[1, 2]]&/@(Times@@@Partition[Prime[Range[ 80]], 2, 1]+1)] (* Harvey P. Dale, Dec 25 2011 *)
|
|
PROG
|
(PARI) p(n) = if (n==0, 1, prime(n));
a(n) = valuation(p(n)*p(n-1) + 1, 2); \\ Michel Marcus, Jun 06 2019
(Magma) p:=PrimesUpTo(10000); sol:=[]; sol[1]:=0; for n in [2..80] do sol[n]:=Valuation(1+p[n]*p[n-1], 2); end for; sol; // Marius A. Burtea, Jun 06 2019
(Python)
from sympy import prime
def A023528(n): return 0 if n == 1 else (~(m:=prime(n)*prime(n-1)+1)& m-1).bit_length() # Chai Wah Wu, Jul 07 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|