RamseyNumber

RamseyNumber(r, s)

returns the Ramsey number R(r,s). Currently not all values are known for 1 <= r <= 4. The function returns unevaluated if the value is unknown.

See

• Wikipedia - Ramsey’s theorem
• OEIS - A212954

Examples

>> Table(RamseyNumber(1,j), {j,1,20})
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

>> Table(RamseyNumber(2,j), {j,1,20})
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

>> Table(RamseyNumber(i,j), {i,1,5},{j,i,10})
{{1,1,1,1,1,1,1,1,1,1},{2,3,4,5,6,7,8,9,10},{6,9,14,18,23,28,36,RamseyNumber(3,10)},{18,25,RamseyNumber(4,6),RamseyNumber(4,7),RamseyNumber(4,8),RamseyNumber(4,9),RamseyNumber(4,10)}}