A270192 Numbers n for which (prime(n+1)-prime(n)) mod 3 = 2.

2, 3, 5, 7, 10, 13, 17, 20, 24, 26, 28, 30, 33, 35, 41, 43, 45, 49, 52, 57, 60, 62, 64, 66, 69, 72, 77, 79, 81, 83, 87, 89, 92, 94, 98, 104, 109, 113, 116, 120, 124, 126, 128, 132, 135, 137, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 162, 166, 171, 173, 176, 178, 182, 186, 190, 192, 196, 201, 206, 209, 212, 215, 220, 223, 225

Offset: 1

Author

Antti Karttunen, Mar 16 2016

Keywords

• nonn

Examples

			2 is present as prime(3) - prime(2) = 5 - 3 = 2 = 2 modulo 3.
24 is present as prime(24) = 89, prime(25) = 97 and 97-89 = 8 = 2 modulo 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A270189.

Positions of 2's in A137264.

Cf. A000040, A001223, A270190, A270191.

Differs from its subsequence A029707 for the first time at n=9.

Programs

Mathematica

Select[Range@ 225, Mod[Prime[# + 1] - Prime@ #, 3] == 2 &] (* Michael De Vlieger, Mar 17 2016 *)
Position[Differences[Prime[Range[300]]],?(Mod[#,3]==2&)]//Flatten (* _Harvey P. Dale, Jul 22 2016 *)

PARI

isok(n) = ((prime(n+1) - prime(n)) % 3) == 2; \\ Michel Marcus, Mar 17 2016