A125164 Positive integers n such that no prime exists of the form (k! + 3n - 1), (k! + 3n) or (k! + 3n + 1) for any k.

11, 21, 25, 31, 39, 41, 47, 51, 53, 61, 67, 69, 71, 73, 81, 91, 95, 99, 101, 107, 109, 111, 113, 121, 123, 125, 131, 135, 137, 141, 145, 151, 157, 161, 165, 171, 175, 177, 179, 181, 183, 191, 193, 201, 203, 207, 209, 211, 221, 223, 229, 231, 235, 237, 241, 243, 245, 249, 251, 255, 259

Offset: 1

Author

Alexander Adamchuk, Nov 22 2006

Keywords

• nonn

Comments

3*a(n) is an index of the middle term in a triple of consecutive zeros in A125162. The indices of zeros in A125162 are listed in A125163.

Primes in this sequence form A115058.

Examples

			Triplets of consecutive terms in A125163: {32,33,34}, {62,63,64}, {74,75,76}, {92,93,94}, {116,117,118}, {122,123,124}, {140,141,142}, {152,153,154}, {158,159,160}, {182,183,184}, {200,201,202}, {206,207,208}, {212,213,214}, {218,219,220}, {242,243,244}, {272,273,274}, {284,285,286}.
		

Crossrefs

Cf. A125162, A125163, A115058.

Programs

Mathematica

Select[Range[2,300],NoneTrue[Flatten[Table[k!+3*#+{-1,0,1},{k,#-1}]],PrimeQ]&] (* Harvey P. Dale, Jun 24 2025 *)

Extensions

Edited and extended by Max Alekseyev, Feb 06 2010