A194831 - OEIS

%I #11 Dec 05 2012 08:03:18

%S 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,

%T 101,104,115,128,133,146,155,169,180,188,194,196,201,209,225,228,248,

%U 250,282,286,325,332,359,391,400,443,449,470,555,579,582,679,741

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

%C 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<<p.

%D See A046927.

%H Hugo Pfoertner, <a href="/A194831/b194831.txt">Table of n, a(n) for n = 1..322</a>

%e 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.

%t 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 *)

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

%K nonn

%O 1,2

%A _Hugo Pfoertner_, Sep 12 2011