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A212888
Conjectured number of positive even numbers that can be represented as the sum of two twin primes p + q in exactly n ways, with p >= q.
2
35, 115, 285, 327, 557, 537, 723, 652, 882, 773, 1061, 916, 1158, 1069, 1369, 1143, 1436, 1307, 1566, 1318, 1711, 1336, 1752, 1380, 1798, 1480, 1847, 1449, 2012, 1556, 1967, 1599, 2184, 1646, 2257, 1656, 2278, 1779, 2376, 1786, 2353, 1823, 2523, 1832, 2415
OFFSET
0,1
COMMENTS
For even n, a(n) - a(n-1) increases as n increases.
MATHEMATICA
p = Prime[Range[10000]]; tp = Select[p, PrimeQ[# + 2] || PrimeQ[# - 2] &]; {tn, t} = Transpose[Sort[Tally[Select[Flatten[Table[If[a >= b, a + b, 0], {a, tp}, {b, tp}]], # < tp[[-1]] &]]]]; Join[{Length[Complement[Range[2, tn[[-1]], 2], tn]]}, Table[Count[t, n], {n, 8}]] (* T. D. Noe, May 30 2012 *)
CROSSREFS
Cf. A001097 (twin primes).
Cf. A007534 (35 numbers that have no representation).
Cf. A129363 (number of partitions of 2n into the sum of two twin primes).
Cf. A212613 (last number having n representations).
Sequence in context: A251269 A268118 A374809 * A044286 A044667 A262455
KEYWORD
nonn
AUTHOR
Michael Jones, May 29 2012
EXTENSIONS
Extended and corrected by T. D. Noe, May 30 2012
STATUS
approved