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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117929 Number of partitions of n into 2 distinct primes. 6
0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 1, 2, 1, 2, 0, 3, 1, 2, 0, 2, 0, 3, 1, 2, 1, 3, 0, 4, 0, 1, 1, 3, 0, 4, 1, 3, 1, 3, 0, 5, 1, 4, 0, 3, 0, 5, 1, 3, 0, 3, 0, 6, 1, 2, 1, 5, 0, 6, 0, 2, 1, 5, 0, 6, 1, 4, 1, 5, 0, 7, 0, 4, 1, 4, 0, 8, 1, 4, 0, 4, 0, 9, 1, 4, 0, 4, 0, 7, 0, 3, 1, 6, 0, 8, 1, 5, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,16

COMMENTS

Number of distinct rectangles with prime length and width such that L + W = n, W < L. For example, a(16) = 2; the two rectangles are 3 X 13 and 5 X 11. - Wesley Ivan Hurt, Oct 29 2017

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

FORMULA

G.f.: Sum_{j>0} Sum_{i=1..j-1} x^(p(i)+p(j)), where p(k) is the k-th prime.

G.f.: A(x)^2/2 - A(x^2)/2 where A(x) = Sum_{p in primes} x^p. - Geoffrey Critzer, Nov 21 2012

a(n) = [x^n*y^2] Product_{i>=1} (1+x^prime(i)*y). - Alois P. Heinz, Nov 22 2012

a(n) = Sum_{i=2..floor((n-1)/2)} A010051(i) * A010051(n-i). - Wesley Ivan Hurt, Oct 29 2017

EXAMPLE

a(24) = 3 because we have [19,5], [17,7] and [13,11].

MAPLE

g:=sum(sum(x^(ithprime(i)+ithprime(j)), i=1..j-1), j=1..35): gser:=series(g, x=0, 130): seq(coeff(gser, x, n), n=1..125);

MATHEMATICA

l = {}; For[n = 1, n <= 1000, n++, c = 0; For[k = 1, Prime[k] < n/2, k++, If[PrimeQ[n - Prime[k]], c = c + 1] ]; AppendTo[l, c] ] l (* Jake Foster, Oct 27 2008 *)

PROG

(PARI) a(n)=my(s); forprime(p=2, (n-1)\2, s+=isprime(n-p)); s \\ Charles R Greathouse IV, Feb 26 2014

CROSSREFS

Cf. A010051, A045917, A061358, A073610.

Column k=2 of A219180. - Alois P. Heinz, Nov 13 2012

Sequence in context: A165414 A178687 A238417 * A107455 A039701 A025822

Adjacent sequences:  A117926 A117927 A117928 * A117930 A117931 A117932

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Apr 03 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 16 02:33 EST 2018. Contains 317252 sequences. (Running on oeis4.)