A052165 Primes at which the difference pattern X,2,4,2,Y (X and Y >= 6) occurs in A001223.

191, 821, 2081, 3251, 9431, 13001, 15641, 18041, 18911, 25301, 31721, 34841, 51341, 62981, 67211, 69491, 72221, 77261, 81041, 82721, 97841, 99131, 109841, 116531, 119291, 122201, 135461, 157271, 171161, 187631, 194861, 201491, 217361

Offset: 1

Author

Labos Elemer, Jan 26 2000

Keywords

• nonn

Comments

All terms == 11 (mod 30). - Robert Israel, Nov 30 2015

Examples

			191 is here because 191 + 2 = 193, 191 + 4 + 2 = 197, 191 + 2 + 4 + 2 = 199 are primes; the prime preceding 191 is 181; the prime following 199 is 211; and the corresponding differences are 10 and 12. Thus the d-pattern "around 191" is {10,2,4,2,12}.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001223, A022008, A047078, A052160, A052162, A052163, A052164, A052167, A052168.

Programs

Maple

Primes:= select(isprime,[2,seq(i,i=3..10^6,2)]):
Gaps:= Primes[2..-1]-Primes[1..-2]:
Primes[select(t -> Gaps[t] = 2 and Gaps[t+1] = 4 and Gaps[t+2] = 2 and Gaps[t-1] >= 6 and Gaps[t+3]>=6, [$2..nops(Gaps)-3])]; # Robert Israel, Nov 30 2015

Mathematica

With[{x = 6, y = 6, s = Partition[#, 6, 1] &@ Prime@ Range[3*10^4]}, Select[s, And[First@ # >= x, Last@ # >= y, Most@ Rest@ # == {2, 4, 2}] &@ Differences@ # &]][[All, 2]] (* Michael De Vlieger, Oct 26 2017 *)