A194830 Odd numbers for which the number of ways to express them as 2*p+q, p,q primes, is a new record.

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

Offset

1,1

Comments

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

References

See A046927.

Links

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

Eric Weisstein's World of Mathematics, Levy's Conjecture

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]] (* Jean-François Alcover, Dec 05 2012 *)

Crossrefs

Cf. A046927, A194831 (size of records).

Sequence in context: A140364 A366526 A022321 * A183344 A255830 A256613

Adjacent sequences: A194827 A194828 A194829 * A194831 A194832 A194833

Keyword

nonn

Author

Hugo Pfoertner, Sep 12 2011

Status

approved