A023512 Exponent of 2 in prime factorization of prime(n) + 1.

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

Offset

1,2

Comments

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

Links

K. G. Stier, Table of n, a(n) for n = 1..2261

Example

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

Maple

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

Mathematica

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 *)

Prog

(Magma) [Valuation(NthPrime(n)+1, 2): n in [1..110]]; // Bruno Berselli, Aug 05 2013
(PARI) a(n)=valuation(prime(n)+1, 2);
vector(100, n, a(n)) \\ Joerg Arndt, Mar 11 2014

Crossrefs

Cf. A239114.

Sequence in context: A255191 A277818 A324607 * A322027 A088192 A218459

Adjacent sequences: A023509 A023510 A023511 * A023513 A023514 A023515

Keyword

nonn

Author

Clark Kimberling

Extensions

Corrected by Yasutoshi Kohmoto, Feb 25 2005

Edited by N. J. A. Sloane, Dec 23 2006

Status

approved