

A072511


Least number m such that 2m can be expressed as the sum of two distinct primes in exactly n ways.


1



1, 4, 8, 12, 18, 24, 30, 39, 42, 45, 57, 72, 60, 84, 90, 117, 123, 144, 120, 105, 162, 150, 180, 237, 165, 264, 288, 195, 231, 240, 210, 285, 255, 336, 396, 378, 438, 357, 399, 345, 519, 315, 504, 465, 390, 480, 435, 462, 450, 567, 717, 420, 495, 651, 540, 615
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OFFSET

0,2


COMMENTS

Let f(x) = A061357(x) be the number of primes p < x such that 2xp is also prime. a(n) is the smallest positive integer x such that f(x) = n.
Or, least number m such that m can be expressed as the mean of two distinct primes in exactly n ways. Cf. A061357 = number of ways n can be expressed as the mean of two distinct primes, A061357 = number of ways the even integer 2n can be written as the sum of two primes for all even integers >6.  Zak Seidov, Sep 08 2006
For what values of n is a(n) > a(n+1)?


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000


FORMULA

It seems that for n>7 n*log(n)*log(log(n)) < a(n) < 3n*log(n)*log(log(n)). Does lim n>infinity a(n)/n/log(n)/log(log(n)) exist ?  Benoit Cloitre, Aug 11 2002


EXAMPLE

a(1)=4 because 8 = 3+5 that is 8 can be expressed as the sum of two distinct primes by exactly 1 way,
a(2)=8 because 16 = 3+13 = 5+11 (2 ways),
a(3)=12 because 24 = 5+17 = 7+17 = 11+17 (3 ways),
a(4)=18 because 36 = 5+31 = 7+29 = 13+23 = 17+19 (4 ways), etc.
Starting with third term 12, all terms are multiples of 3.


MATHEMATICA

f[x_] := Length[Select[2x(Prime/@Range[PrimePi[x1]]), PrimeQ]]; For[x=1, x<1000, x++, fx=f[x]; If[a[fx]>=0, Null, Null, a[fx]=x]]; a/@Range[0, 60]


PROG

(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a072511 = (+ 1) . fromJust . (`elemIndex` a061357_list)
 Reinhard Zumkeller, Nov 10 2012


CROSSREFS

Cf. A061357, A061357.
Sequence in context: A311634 A311635 A049621 * A156324 A311636 A311637
Adjacent sequences: A072508 A072509 A072510 * A072512 A072513 A072514


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Jul 24 2002


EXTENSIONS

Edited by Dean Hickerson, Aug 07 2002
Entry revised by N. J. A. Sloane, Sep 12 2006


STATUS

approved



