A023512 - OEIS

%I #28 Sep 08 2022 08:44:47

%S 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,

%T 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,

%U 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

%N Exponent of 2 in prime factorization of prime(n) + 1.

%C 2^a(n) is the largest power of 2 dividing (prime(n)+1).

%H K. G. Stier, <a href="/A023512/b023512.txt">Table of n, a(n) for n = 1..2261</a>

%e a(9)=3 because the 9th prime is 23 and the largest power of 2 dividing 24 is 3.

%p 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

%t Join[{0}, Table[FactorInteger[Prime[n] + 1][[1]][[2]], {n, 2, 100}]] (* _Clark Kimberling_, Oct 01 2013 *)

%t IntegerExponent[Prime[Range[100]] + 1, 2] (* _Zak Seidov_, Apr 25 2014 *)

%o (Magma) [Valuation(NthPrime(n)+1, 2): n in [1..110]]; // _Bruno Berselli_, Aug 05 2013

%o (PARI) a(n)=valuation(prime(n)+1,2);

%o vector(100,n,a(n)) \\ _Joerg Arndt_, Mar 11 2014

%Y Cf. A239114.

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Corrected by _Yasutoshi Kohmoto_, Feb 25 2005

%E Edited by _N. J. A. Sloane_, Dec 23 2006