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

 

Logo

The October issue of the Notices of the Amer. Math. Soc. has an article about the OEIS.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A115230 Let p = prime(n); a(n) = number of ways to write p = 2^i + q^j where i >= 0, j >= 1, q = odd prime. 5
1, 1, 2, 2, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 2, 3, 2, 2, 3, 2, 4, 3, 2, 2, 2, 2, 2, 4, 1, 3, 3, 4, 0, 2, 3, 1, 3, 3, 1, 4, 1, 1, 2, 4, 2, 1, 3, 3, 2, 1, 3, 1, 3, 2, 1, 3, 2, 2, 3, 4, 2, 1, 2, 2, 0, 1, 3, 2, 4, 2, 2, 0, 2, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 3, 3, 0, 2, 3, 2, 1, 1, 3, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..105.

FORMULA

a(n) = sum(A036987(k-1)*A000035(p-k)*A010055(p-k): 1<=k<p, p=prime(n)). [Reinhard Zumkeller, Apr 29 2010]

EXAMPLE

n=25: A000040(25) = 97 = 2^6+3*11 = 2^5+5*13 = 2^4+3^4 = 2^3+89^1 = 2^2+3*31 = 2^1+5*19 = 2^0+3*2^5, therefore a(25)=#{[16+81],[8+89]}=2.

MAPLE

From Reinhard Zumkeller, Apr 30 2010: (Start)

A000035 := proc(n) n mod 2 ; end proc:

A000108 := proc(n) binomial(2*n, n)/(n+1) ; end proc:

A036987 := proc(n) A000108(n) mod 2 ; end proc:

A010055 := proc(n) if n = 1 then 1; else numtheory[factorset](n) ; if nops(%) = 1 then 1; else 0; end if; end if: end proc:

A115230 := proc(n) p := ithprime(n) ; add(A036987(k-1)*A000035(p-k)*A010055(p-k), k=1..p-1) ; end proc: seq(A115230(n), n=1..40) ; # R. J. Mathar, Apr 30 2010 (End)

MATHEMATICA

f[p_] := Length@ Table[q = p - 2^exp; If[ PrimeNu@ q == 1, {q}, Sequence @@ {}], {exp, 0, Floor@ Log2@ p}]; Table[ f[ Prime[ n]], {n, 105}] (* Robert G. Wilson v, Oct 05 2014 *)

CROSSREFS

Cf. A115231-A115233, A000079, A061345.

Sequence in context: A253315 A210480 A266123 * A304733 A165024 A300402

Adjacent sequences:  A115227 A115228 A115229 * A115231 A115232 A115233

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 17 2006

EXTENSIONS

Recomputed by Charles R Greathouse IV, Ray Chandler, R. J. Mathar, and Reinhard Zumkeller, Apr 29 2010; thanks to Charles R Greathouse IV, who pointed out that there were many errors in entries of A115230-A115233.

Edited by N. J. A. Sloane, Apr 30 2010

Formula corrected, thanks to R. J. Mathar who found an error in it Reinhard Zumkeller, Apr 30 2010

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 September 25 11:05 EDT 2018. Contains 315389 sequences. (Running on oeis4.)