A244264 Positive integers n such that all the gaps prime(n+i+1) - prime(n+i) (i = 0..7) are powers of two.

1, 330, 331, 231045, 324589, 469622, 1115943, 1320087, 1989982, 2376837, 2947716, 3004877, 3129744, 4222944, 4232547, 4395993, 4549061, 4831827, 5019310, 5131215, 6415331, 7036512, 8699278, 9490487, 10252155

Offset

1,2

Comments

Conjecture: For any integer m > 0, there are infinitely many positive integers n such that all the gaps prime(n+i+1) - prime(n+i) (i = 0, ..., m-1) are powers of two.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..200

Example

a(1) = 1 since all those prime(2) - prime(1) = 3 - 2 = 1, prime(3) - prime(2) = 5 - 3 = 2, prime(4) - prime(3) = 7 - 5 = 2, prime(5) - prime(4) = 11 - 7 = 4, prime(6) - prime(5) = 13 - 11 = 2, prime(7) - prime(6) = 17 - 13 = 4 and prime(8) - prime(7) = 19 - 17 = 2 are powers of two.

Mathematica

PowQ[n_]:=n==2^(IntegerExponent[n, 2])
m=0; Do[Do[If[PowQ[Prime[n+i+1]-Prime[n+i]]==False, Goto[aa]], {i, 0, 7}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 10252155}]

Crossrefs

Cf. A000040, A000079, A244254.

Sequence in context: A145274 A174848 A300009 * A117345 A237189 A064262

Adjacent sequences: A244261 A244262 A244263 * A244265 A244266 A244267

Keyword

nonn

Author

Zhi-Wei Sun, Jun 24 2014

Status

approved