A123123 Numbers m such that m mod k = 2 for only one integer k in 2..m.

5, 6, 7, 9, 13, 15, 19, 21, 25, 31, 33, 39, 43, 45, 49, 55, 61, 63, 69, 73, 75, 81, 85, 91, 99, 103, 105, 109, 111, 115, 129, 133, 139, 141, 151, 153, 159, 165, 169, 175, 181, 183, 193, 195, 199, 201, 213, 225, 229, 231, 235, 241, 243, 253, 259, 265, 271, 273, 279

Offset: 1

Author

Jared B. Ricks (jaredricks(AT)yahoo.com), Sep 24 2006

Keywords

• nonn

Comments

From 7 on, sequence gives primes + two. This can be easily seen since the definition is equivalent to the following: "Numbers m such that there's only one k, 2 <= k <= m-2, that divides m-2." So k|(m-2) and values of k: m and m-1 are not considered since they don't divide m-2. But this 2nd statement is also the same as saying that m-2 is a prime number and so m = prime + 2.

Essentially the same as A048974. - R. J. Mathar, Jun 18 2008

Crossrefs

Cf. A000040, A048974.

Programs

Mathematica

Join[{5,6},Prime[Range[3,60]]+2] (* Harvey P. Dale, Sep 05 2017 *)

PARI

for(n=1,500,if(sum(k=2,n,if(n%k==2,1,0))==1,print1(n,", ")))

Python

from sympy import prime
a = lambda n : 5 if n==1 else (6 if n==2 else prime(n)+2)
# Christoph B. Kassir, Apr 14 2022

Formula

a(n) = prime(n) + 2 = A000040(n) + 2 for n >= 3 (prime(3) = 5 > 4).

Extensions

Edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 24 2006