A125211 -id:A125211 - cp's OEIS frontend

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

Alexander Adamchuk, Nov 23 2006

nonn

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.

			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}.

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

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.

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

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

A125213 Integers m such that no prime exists of the form abs(k! - 3m - 1), abs(k! - 3m), or abs(k! - 3m + 1).

Original entry on oeis.org

17, 19, 29, 31, 45, 49, 57, 59, 63, 69, 73, 79, 83, 85, 87, 89, 97, 99, 101, 107, 109, 115, 119, 121, 129, 131, 135, 139, 143, 149, 151, 157, 159, 161, 165, 169, 171, 173, 177, 179, 185, 187, 189, 195, 197, 199, 209, 213, 217, 219, 223, 227, 229, 233, 235, 249, 255, 259

Offset: 1

Alexander Adamchuk, Nov 23 2006

nonn

3*a(n) are the indices of the middle terms in the triples of consecutive zeros in A125211. The middle index of most consecutive zero triples in A125211 is odd and is a multiple of 3.

			Triplets of consecutive zeros in A125211: {50,51,52}, {56,57,58}, {86,87,88}, {92,93,94}, ...

Cf. A125162, A125163, A125164, A125211, A125212.

Edited and extended by Max Alekseyev, Feb 10 2010

cp's OEIS Frontend

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

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