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.

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

Author

Michael Jones, May 29 2012

Keywords

• nonn

Comments

For even n, a(n) - a(n-1) increases as n increases.

Links

• T. D. Noe, Table of n, a(n) for n = 0..100

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).

Programs

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 *)

Extensions

Extended and corrected by T. D. Noe, May 30 2012