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

1,1

Comments

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

Links

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

Example

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}.

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 *)

Crossrefs

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

Sequence in context: A086878 A082445 A108848 * A103733 A217500 A142451

Adjacent sequences: A052162 A052163 A052164 * A052166 A052167 A052168

Keyword

nonn

Author

Labos Elemer, Jan 26 2000

Status

approved