A125212 -id:A125212 - cp's OEIS frontend

A125211 a(n) = total number of primes of the form |k! - n|.

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, 1, 2, 0, 0, 0, 7, 1, 11, 1, 1, 0, 2, 0, 9, 1, 1, 0, 9, 1, 11, 1, 1, 0, 4, 0, 11, 1, 1, 0, 8, 1, 3, 0, 0, 0, 14, 1, 3, 0, 0, 0, 2, 0, 11, 1, 1, 0, 9

Offset: 1

Alexander Adamchuk, Nov 23 2006

nonn

Numbers n such that a(n) = 0 are listed in A125212(n) = {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,...} Numbers n such that no prime exists of the form k! - n. Note the triples of consecutive zeros in a(n) for n = {{50,51,52}, {56,57,58}, {86,87,88}, {92,93,94}, ...}. Most zeros in a(n) have even indices. The middle index of most consecutive zero triples 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(n) = {17,19,29,31,45,49,57,59,63,69,73,79,83,85,87,89,97,99,...}. 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 a(n): a(324)-a(330) = 0.

			a(4) = 3 because there are 3 primes of the form |k! - 4|:
1! - 4 = -3, 2! - 4 = -2, 3! - 4 = 2.
k! - 4 is composite for all k>3 because it is divisible by 4.

Amiram Eldar, Table of n, a(n) for n = 1..2500

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. A125212, A125213.

Table[Length[Select[Range[n],PrimeQ[ #!-n]&]],{n,1,300}]

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

A125211 a(n) = total number of primes of the form |k! - n|.

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