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

Author

Zhi-Wei Sun, Apr 25 2015

Keywords

• nonn

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.

Examples

			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.
		

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.

Crossrefs

Cf. A014574, A256707, A257317.

Programs

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}]