A070542 Numbers n such that binomial(2n,n) does not have two prime factors that add to 2n.

1, 2, 3, 4, 6, 10, 15, 26, 28, 64

Offset

1,2

Comments

No others for n <= 36000. - Naohiro Nomoto, May 11 2002

No others for n <= 200000. - T. D. Noe, May 22 2002

No others for n <= 10^6. - T. D. Noe, Nov 29 2003

No others for n < 10^8. It is conjectured that there are no other n with this property. - T. D. Noe, Dec 23 2004

Links

Table of n, a(n) for n=1..10.

Example

6 is in the sequence because binomial(12,6) = 924, whose prime factors are 2, 3, 7 and 11. None of these primes, added pairwise, yield 12.

Mathematica

minN=1; maxN=100000; lst={}; isPrime=Table[If[PrimeQ[i], True, False], {i, 2maxN}]; c=Binomial[2minN-2, minN-1]; For[n=minN, n<=maxN, n++, c=(c(4n-2))/n; (* Binomial[2n, n] *) found=False; k=3; While[ !found&&k<=n, If[isPrime[[k]]&&isPrime[[2n-k]], If[Mod[c, k]==0, found=True]]; k=k+2]; If[ !found, AppendTo[lst, n]]]; lst

Crossrefs

Cf. A000984, A127499.

Sequence in context: A221995 A364587 A221996 * A098855 A143283 A104767

Adjacent sequences: A070539 A070540 A070541 * A070543 A070544 A070545

Keyword

nonn

Author

T. D. Noe, May 02 2002

Status

approved