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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-Fran├žois Alcover, Dec 05 2012 *)

CROSSREFS

Cf. A046927, A194831 (size of records).

Sequence in context: A250292 A140364 A022321 * A183344 A255830 A256613

Adjacent sequences:  A194827 A194828 A194829 * A194831 A194832 A194833

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Sep 12 2011

STATUS

approved

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Last modified July 1 12:30 EDT 2022. Contains 354973 sequences. (Running on oeis4.)