

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
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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

ZhiWei Sun, Table of n, a(n) for n = 1..10000
ZhiWei 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*21,9*0+3*2+1} = {5,7} is a twin prime pair.
a(2) = 1 since {9*1+3*11,9*1+3*1+1} = {11,13} is a twin prime pair.
a(3) = 2 since {9*2+3*01,9*2+3*0+1} = {17,19} is a twin prime pair.


MATHEMATICA

TQ[m_]:=PrimeQ[3m1]&&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

ZhiWei Sun, Apr 25 2015


STATUS

approved



