A374691 The smallest m+k such that n can be written as n=binomial(m,k).

0, 3, 4, 5, 6, 6, 8, 9, 10, 7, 12, 13, 14, 15, 8, 17, 18, 19, 20, 9, 9, 23, 24, 25, 26, 27, 28, 10, 30, 31, 32, 33, 34, 35, 10, 11, 38, 39, 40, 41, 42, 43, 44, 45, 12, 47, 48, 49, 50, 51, 52, 53, 54, 55, 13, 11, 58, 59, 60, 61, 62, 63, 64, 65, 66, 14, 68, 69, 70, 12, 72, 73, 74, 75, 76, 77, 78, 15, 80, 81

Offset: 1

Author

R. J. Mathar, Jul 16 2024

Keywords

• nonn
• easy

Comments

This is most often a(n) = n+1 because the n that do not appear in the "main" body of the Pascal Triangle appear at last at k=1.

Examples

			Searching along upwards diagonals, the 6 appears first at 6=binomial(4,2) with m+k=4+2=6, so a(6)=6. The 10 appears first at 10=binomial(5,2) with m+k=7, so a(10)=7.
		

Crossrefs

Cf. A022911, A022912.

Programs

Maple

A374691 := proc(n)
    local mk,k,m ;
    for mk from 0 to n+1 do
        for k from 0 to mk/2 do
            m := mk-k ;
            if binomial(m,k) = n then
                return mk ;
            end if;
        end do:
    end do:
    return -1 ;
end proc:
seq( A374691(n),n=1..80) ;