A244294 Positive integers n such that (prime(n+i+1) - prime(n+i))/2 is prime for every i = 0, ..., 12.

56290, 110172, 127202, 377050, 469555, 775074, 929251, 2249530, 2249531, 2995058, 2995059, 4011471, 4011472, 4469958, 4778861, 4825822, 4825823, 4876245, 4881979, 4901245

Offset

1,1

Comments

Conjecture: For any integer m > 0, there are infinitely many positive integers n such that (prime(n+i+1) - prime(n+i))/2 is prime for every i = 0, ..., m-1.

Note that for n = 10377594 all those (prime(n+i+1) - prime(n+i))/2 (i = 0, ..., 15) are prime.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..93

Example

 a(1) = 56290 with (prime(56290+i+1) - prime(56290+i))/2 (i=0..12) having prime values 5, 3, 3, 7, 3, 5, 7, 11, 19, 2, 3, 3, 3 respectively.

Mathematica

d[n_]:=(Prime[n+1]-Prime[n])/2
m=0; Do[Do[If[PrimeQ[d[n+i]]==False, Goto[aa]], {i, 0, 12}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 4901245}]

Crossrefs

Cf. A000040, A244254, A244264, A244266.

Sequence in context: A031655 A203964 A198165 * A234488 A348100 A184613

Adjacent sequences: A244291 A244292 A244293 * A244295 A244296 A244297

Keyword

nonn

Author

Zhi-Wei Sun, Jun 25 2014

Status

approved