A125212 Numbers m such that no prime exists of the form |k! - m|; or A125211(m) = 0.

1, 2, 10, 16, 28, 34, 36, 40, 46, 50, 51, 52, 56, 57, 58, 64, 66, 70, 76, 78, 82, 86, 87, 88, 92, 93, 94, 96, 100, 106, 112, 116, 120, 124, 126, 130, 134, 135, 136, 142, 144, 146, 147, 148, 154, 156, 160, 162, 166, 170, 171, 172, 176, 177, 178, 184, 186, 188, 189

Offset: 1

Author

Alexander Adamchuk, Nov 23 2006

Keywords

• nonn

Comments

Note the triples of consecutive zeros in A125211 for n = {{50,51,52}, {56,57,58}, {86,87,88}, {92,93,94}, ...}. Most zeros in A125211 have even indices. The middle index of most consecutive zero triples in A125211 is odd and is a multiple of 3. Numbers n such that no prime exists of the form (k! - 3n - 1), (k! - 3n), (k! - 3n + 1) are listed in A125213. The first pair of odd middle indices of zero triples that are not divisible by 3 is n = 325 and n = 329. They belong to the first septuplet of consecutive zeros in A125211. A125211(n) = 0 for 7 consecutive terms from n = 324 to n = 330.

Examples

			A125211 begins {0,0,2,3,2,1,3,2,2,0,5,1,7,1,1,0,9,1,6,1,2,1,4,1,2,1,1,0,5,1,8,1,1,0,2,0,10,1,1,0,6,1,10,1,1,0,10,1,3,0,0,0,7,...}.
Thus a(1) = 1, a(2) = 2, a(3) = 10, a(10)-a(12) = {50,51,52}.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A125162 (number of primes of the form k! + n).

Cf. A125163 (numbers n such that no prime exists of the form k! + n).

Cf. A125164 (numbers n such that no prime exists of the form (k! + 3n - 1), (k! + 3n), (k! + 3n + 1)).

Cf. A125211, A125213.

Programs

Mathematica

k={};Do[If[Length[Select[Range[m],PrimeQ[#!-m]&]]==0,AppendTo[k,m]],{m,189}];k (* James C. McMahon, Dec 16 2024 *)

PARI

isok(m)={for(k=1, m-1, if(isprime(abs(k!-m)), return(0))); 1} \\ Andrew Howroyd, Dec 16 2024