

A194830


Odd numbers for which the number of ways to express them as 2*p+q, p,q primes, is a new record.


4



7, 9, 17, 33, 45, 51, 75, 93, 105, 135, 153, 165, 225, 273, 285, 315, 405, 465, 495, 525, 735, 765, 945, 1155, 1365, 1785, 1995, 2145, 2415, 2625, 3045, 3255, 3465, 3885, 4095, 4305, 4725, 4935, 5145, 5355, 5565, 5775, 6405, 6825, 7665, 8085, 8925, 9555
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OFFSET

1,1


COMMENTS

2*(positions of records in A046927)+1. The corresponding new record number of representations is given in A194831.


REFERENCES



LINKS



EXAMPLE

a(3)=17, because it can be represented in A194831(3)=4 different ways (17=2*2+13=2*3+11=2*5+7=2*7+3), whereas all smaller odd numbers can only be represented in a smaller number of ways.


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; A194830 = Reap[Do[If[ways[n] > record, record = ways[n]; Print["2n+1 = ", 2n + 1, " record = ", record]; Sow[{ways[n], 2n + 1}]], {n, 0, 12000}]][[2, 1]][[All, 2]] (* JeanFrançois Alcover, Dec 05 2012 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



