A194831 Records in the number of ways to express an odd number as a sum 2*p+q, with p, q primes.

1, 2, 4, 5, 6, 7, 8, 11, 12, 13, 14, 16, 21, 22, 26, 27, 31, 32, 35, 43, 48, 52, 65, 77, 87, 101, 104, 115, 128, 133, 146, 155, 169, 180, 188, 194, 196, 201, 209, 225, 228, 248, 250, 282, 286, 325, 332, 359, 391, 400, 443, 449, 470, 555, 579, 582, 679, 741

Offset: 1

Author

Hugo Pfoertner, Sep 12 2011

Keywords

• nonn

Comments

Records in A046927. The growth rate of this sequence makes the slow growth of A194829 plausible, i.e. 2*n+1 can be represented by 2*p+q with q<

Examples

			a(1)=1: A194830(1)=7 has 1 representation 7=2*2+3; a(2)=2 representations of A194830(2)=9=2*2+5=2*3+3; a(3)=4 representations of A194830(3)=17=2*2+13=2*3+11=2*5+7=2*7+3.
		

References

• See A046927.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..322

Crossrefs

Cf. A194830 [record-setting numbers], A046927, A194828, A194829.

Programs

Mathematica

ways[n_] := ways[n] = (w = 0; Do[ p = 2k + 1; q = n - k; If[PrimeQ[p] && PrimeQ[q], w++], {k, 1, n}]; w); record = 0; A194831 = Reap[Do[If[ways[n] > record, record = ways[n]; Print["2n+1 = ", 2n + 1, " record = ", record]; Sow[{ways[n], n}]], {n, 0, 12000}]][[2, 1]][[All, 1]] (* Jean-François Alcover, Dec 05 2012 *)

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