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

%I A374691 #4 Jul 16 2024 15:30:51
%S A374691 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,
%T A374691 10,30,31,32,33,34,35,10,11,38,39,40,41,42,43,44,45,12,47,48,49,50,51,
%U A374691 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
%N A374691 The smallest m+k such that n can be written as n=binomial(m,k).
%C A374691 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.
%e A374691 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.
%p A374691 A374691 := proc(n)
%p A374691     local mk,k,m ;
%p A374691     for mk from 0 to n+1 do
%p A374691         for k from 0 to mk/2 do
%p A374691             m := mk-k ;
%p A374691             if binomial(m,k) = n then
%p A374691                 return mk ;
%p A374691             end if;
%p A374691         end do:
%p A374691     end do:
%p A374691     return -1 ;
%p A374691 end proc:
%p A374691 seq( A374691(n),n=1..80) ;
%Y A374691 Cf. A022911, A022912.
%K A374691 nonn,easy
%O A374691 1,2
%A A374691 _R. J. Mathar_, Jul 16 2024