login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2017 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let f(x) = A061357(x) be the number of primes p < x such that 2x-p 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[x-1]]), 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

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 10 05:49 EST 2018. Contains 318044 sequences. (Running on oeis4.)