login
A129363
Number of partitions of 2n into the sum of two twin primes.
16
0, 0, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 3, 3, 2, 1, 2, 2, 3, 4, 2, 1, 2, 1, 2, 3, 3, 2, 2, 1, 2, 4, 3, 3, 4, 2, 2, 3, 2, 2, 4, 2, 0, 0, 0, 2, 4, 3, 2, 2, 2, 4, 6, 3, 3, 5, 3, 1, 2, 1, 2, 4, 2, 1, 2, 2, 4, 5, 3, 2, 4, 3, 3, 4, 2, 2, 4, 2, 3, 6, 3, 1, 2, 1, 3, 6, 4, 2, 2, 1, 2, 4, 3, 4, 6, 4, 4, 5, 3, 6, 12
OFFSET
1,5
COMMENTS
a(n/2)=0 for the n in A007534. The logarithmic plot of this sequence seems very regular after 200000 terms.
LINKS
James Grime and Brady Haran, Goldbach Conjecture (but with TWIN PRIMES), Numberphile video (2024)
FORMULA
a(n) = Sum_{i=1..n} ceiling((A010051(i+2) + A010051(i-2))/2) * ceiling((A010051(2n-i+2) + A010051(2n-i-2))/2) * A010051(2n-i) * A010051(i). - Wesley Ivan Hurt, Jan 30 2014
a(n) = sum(A164292(2*n - A001097(k)): A001097(k) <= n). - Reinhard Zumkeller, Feb 03 2014
EXAMPLE
a(11)=3 because 22 = 3+19 = 5+17 = 11+11.
MATHEMATICA
nn=1000; tw=Select[Prime[Range[PrimePi[nn]]], PrimeQ[ #+2]&]; tw=Union[tw, tw+2]; tc=Table[0, {nn}]; tc[[tw]]=1; Table[cnt=0; k=1; While[tw[[k]]<=n/2, cnt=cnt+tc[[n-tw[[k]]]]; k++ ]; cnt, {n, 2, nn, 2}]
PROG
(Haskell)
a129363 n = sum $ map (a164292 . (2*n -)) $ takeWhile (<= n) a001097_list
-- Reinhard Zumkeller, Feb 03 2014
CROSSREFS
Cf. A175931 (n for which a(n-1), a(n), a(n+1) are equal).
Sequence in context: A160089 A259358 A290086 * A308342 A303399 A053597
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 11 2007
EXTENSIONS
Comment converted to crossref by Klaus Brockhaus, Oct 27 2010
STATUS
approved