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A023512
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Exponent of 2 in prime factorization of prime(n) + 1.
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10
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0, 2, 1, 3, 2, 1, 1, 2, 3, 1, 5, 1, 1, 2, 4, 1, 2, 1, 2, 3, 1, 4, 2, 1, 1, 1, 3, 2, 1, 1, 7, 2, 1, 2, 1, 3, 1, 2, 3, 1, 2, 1, 6, 1, 1, 3, 2, 5, 2, 1, 1, 4, 1, 2, 1, 3, 1, 4, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 1, 1, 3, 4, 1, 2, 7, 1, 1, 1, 1, 2, 1, 4, 1, 3, 2, 1, 1, 1, 4, 2, 5, 3, 2, 2, 3, 1, 1, 2, 1, 2, 1, 2, 1, 2
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OFFSET
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1,2
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COMMENTS
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2^a(n) is the largest power of 2 dividing (prime(n)+1).
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LINKS
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EXAMPLE
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a(9)=3 because the 9th prime is 23 and the largest power of 2 dividing 24 is 3.
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MAPLE
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with(numtheory): a:=proc(n) local div, s, j, c: div:=divisors(1+ithprime(n)): s:=nops(div): for j from 1 to s do if type(simplify(log[2](div[j])), integer)=true then c[j]:=simplify(log[2](div[j])) else c[j]:=0 fi od: max(seq(c[j], j=1..s)) end: seq(a(n), n=1..120); # most probably not the simplest Maple program - Emeric Deutsch, Jul 20 2005
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MATHEMATICA
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Join[{0}, Table[FactorInteger[Prime[n] + 1][[1]][[2]], {n, 2, 100}]] (* Clark Kimberling, Oct 01 2013 *)
IntegerExponent[Prime[Range[100]] + 1, 2] (* Zak Seidov, Apr 25 2014 *)
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PROG
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(Magma) [Valuation(NthPrime(n)+1, 2): n in [1..110]]; // Bruno Berselli, Aug 05 2013
(PARI) a(n)=valuation(prime(n)+1, 2);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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