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 A257121 Numbers m with 9*m + 3*r - 1 and 9*m + 3*r + 1 twin prime for some r = 0,1,2. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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 A190203 Adjacent sequences:  A257118 A257119 A257120 * A257122 A257123 A257124 KEYWORD nonn AUTHOR Zhi-Wei Sun, Apr 25 2015 STATUS approved

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Last modified January 27 15:47 EST 2021. Contains 340467 sequences. (Running on oeis4.)