A257121 Numbers m with 9*m + 3*r - 1 and 9*m + 3*r + 1 twin prime for some r = 0,1,2.

0, 1, 2, 3, 4, 6, 8, 11, 12, 15, 16, 20, 21, 22, 25, 26, 30, 31, 34, 38, 46, 48, 51, 58, 63, 66, 68, 71, 73, 90, 91, 92, 95, 98, 113, 114, 116, 118, 121, 128, 136, 142, 143, 144, 146, 158, 161, 164, 165, 178, 180, 185, 188, 191, 198, 208, 214, 216, 222, 225, 231, 232, 234, 236, 238, 248, 252, 256, 260, 264, 283, 288, 295, 298, 301, 303, 310, 311, 330, 333

Offset

1,3

Comments

By the conjecture in A257317, any positive integer should be the sum of two distinct terms of the current sequence one of which is even.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Zhi-Wei Sun, Natural numbers represented by floor(x^2/a) + floor(y^2/b) + floor(z^2/c), arXiv:1504.01608 [math.NT], 2015.

Example

a(1) = 0 since {9*0+3*2-1,9*0+3*2+1} = {5,7} is a twin prime pair.
a(2) = 1 since {9*1+3*1-1,9*1+3*1+1} = {11,13} is a twin prime pair.
a(3) = 2 since {9*2+3*0-1,9*2+3*0+1} = {17,19} is a twin prime pair.

Mathematica

TQ[m_]:=PrimeQ[3m-1]&&PrimeQ[3m+1]
PQ[m_]:=TQ[3*m]||TQ[3*m+1]||TQ[3*m+2]
n=0; Do[If[PQ[m], n=n+1; Print[n, " ", m]], {m, 0, 340}]

Crossrefs

Cf. A014574, A256707, A257317.

Sequence in context: A306802 A293635 A123586 * A039500 A160649 A341059

Adjacent sequences: A257118 A257119 A257120 * A257122 A257123 A257124

Keyword

nonn

Author

Zhi-Wei Sun, Apr 25 2015

Status

approved