A117368 a(n) = largest prime less than the smallest prime dividing (2n-1).

2, 3, 5, 2, 7, 11, 2, 13, 17, 2, 19, 3, 2, 23, 29, 2, 3, 31, 2, 37, 41, 2, 43, 5, 2, 47, 3, 2, 53, 59, 2, 3, 61, 2, 67, 71, 2, 5, 73, 2, 79, 3, 2, 83, 5, 2, 3, 89, 2, 97, 101, 2, 103, 107, 2, 109, 3, 2, 5, 7, 2, 3, 113, 2, 127, 5, 2, 131, 137, 2, 7, 3, 2, 139, 149, 2, 3, 151, 2, 5, 157, 2

Offset: 2

Author

Leroy Quet, Mar 10 2006

Keywords

• nonn

Comments

Placing a 1 between each term of this sequence gets sequence A117365.

Examples

			a(13) = 3 because smallest prime dividing 25 is 5 and largest prime less than 5 is 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A006512, A090368, A117365, A151799.

Programs

Maple

with(numtheory): a:=proc(n): prevprime(factorset(2*n-1)[1]): end: seq(a(n),n=2..90); # Emeric Deutsch, Apr 22 2006

Mathematica

prs=Prime[Range[50]];
f[n_]:=NextPrime[First[Select[prs,Divisible[2 n-1,#]&]],-1]
f/@Range[2,90]  (* Harvey P. Dale, Jan 23 2011 *)

Formula

From Robert Israel, Apr 14 2019: (Start)

a(n) = A151799(A090368(n)).

a(n) = 2*n-3 if 2*n-1 is in A006512. (End)

Extensions

More terms from Emeric Deutsch, Apr 22 2006