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

0,1

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

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: A110832 A251269 A268118 * A044286 A044667 A262455

Adjacent sequences: A212885 A212886 A212887 * A212889 A212890 A212891

Keyword

nonn

Author

Michael Jones, May 29 2012

Extensions

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

Status

approved