A051771 -id:A051771 - cp's OEIS frontend

A051735 Binomial coefficients C(n,k) such that C(n,k)-1 and C(n,k)+1 are twin primes and 2<=k<=floor(n/2).

6, 462, 1877405874732108, 38650751381832, 10000119226331142599460, 51913710643776705684835560, 42552226353687619569660660, 1656627950725900171898183550, 315676747963758694790502389846048040560005901701920, 3571770735028382091998706667681023581492775768

Offset: 0

Joe DeMaio (jdemaio(AT)kennesaw.edu), Dec 06 1999

nonn

Sequence is ordered by size of n not size of C(n,k). Link gives list of all values up to n=1352.

			C(11,5)=462 is a member of the sequence because 461 and 463 are twin primes.

More terms

See A051770 for values of n, A051771 for values of k.

Select[Flatten[Table[Binomial[n,k],{n,200},{k,2,Floor[n/2]}]], AllTrue[ #+ {1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 10 2015 *)

More terms from Harvey P. Dale, Dec 10 2015

A051770 Numbers n such that there exists a binomial coefficient C(n,k) where C(n,k)-1 and C(n,k)+1 are twin primes and 2<=k<=floor(n/2).

Original entry on oeis.org

4, 11, 54, 69, 77, 89, 91, 155, 173, 199, 202, 202, 208, 218, 245, 272, 286, 293, 293, 323, 324, 347, 368, 370, 373, 379, 413, 489, 512, 514, 533, 549, 552, 558, 637, 650, 674, 731, 749, 759, 771, 773, 782, 783, 787, 811, 849, 850, 883, 896, 902, 927, 937

Offset: 1

Joe DeMaio (jdemaio(AT)kennesaw.edu), Dec 08 1999

nonn

The integer 202 occurs twice because both C(202,34) and C(202,69) yield twin prime pairs.

			The integer 11 is a member of the sequence because C(11,5)=462 and 461 and 463 are twin primes.

Source

A051735, A051771.

cp's OEIS Frontend

A051735 Binomial coefficients C(n,k) such that C(n,k)-1 and C(n,k)+1 are twin primes and 2<=k<=floor(n/2).

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