The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60, we have over 367,000 sequences, and we’ve crossed 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 04:09 EST 2023. Contains 367505 sequences. (Running on oeis4.)