A244308 Positive integers n such that all the gaps prime(n+i+1) - prime(n+i) (i = 0, ..., 12) belong to the set {g > 0: g - 1 and g + 1 are twin prime}.

754205, 1347541, 1347542, 1347543, 1347544, 1347545, 1692355, 2067412, 2067413, 2067414, 2067415, 2218613, 2809181, 5455635, 6127765, 6127766, 7034825, 7034826, 7194143, 8603331, 8815168, 8815169, 8815170, 8815171, 9072188

Offset

1,1

Comments

Conjecture: For any integer m > 0, there are infinitely many positive integers n such that all those gaps prime(n+i+1) - prime(n+i) (i = 0, ..., m-1) belong to the set {g > 0: g - 1 and g + 1 are twin prime}.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..50

Example

a(1) = 754205 with those prime(754205+i+1) - prime(754205+i) (i = 0, ..., 12) having respective values 4, 12, 18, 42, 30, 30, 6, 12, 18, 30, 18, 12, 12 in the set {g > 0: g - 1 and g + 1 are twin prime}.

Mathematica

d[n_]:=Prime[n+1]-Prime[n]
m=0; Do[Do[If[PrimeQ[d[n+i]-1]==False||PrimeQ[d[n+i]+1]==False, Goto[aa]], {i, 0, 12}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 9072188}]

Crossrefs

Cf. A000040, A014574, A244254, A244264, A244266, A244294.

Sequence in context: A253374 A204229 A290161 * A273971 A259305 A172586

Adjacent sequences: A244305 A244306 A244307 * A244309 A244310 A244311

Keyword

nonn

Author

Zhi-Wei Sun, Jun 25 2014

Status

approved