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A052165 Primes at which the difference pattern X,2,4,2,Y (X and Y >= 6) occurs in A001223. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 16 15:17 EST 2020. Contains 331961 sequences. (Running on oeis4.)