cp's OEIS Frontend

A360587 a(n) is the least positive integer k such that k*(k+1)*...*(k+n-1) does not contain the digit 2, or -1 if there is no such k.

%I A360587 #4 Feb 16 2023 05:40:31
%S A360587 1,2,1,3,7,2,1,3,3,2,1,1,3,2,1,5,10,10,10,17,4,8,38,38,19,17,2,1,1,3
%N A360587 a(n) is the least positive integer k such that k*(k+1)*...*(k+n-1) does not contain the digit 2, or -1 if there is no such k.
%C A360587 a(n) is the least positive integer k such that (k+n-1)!/(k-1)! does not contain the digit 2, or -1 if there is no such k.
%C A360587 a(32) = 13.
%C A360587 Conjecture: a(n) = -1 for n = 31 and all n >= 33.
%e A360587 a(4) = 3 because 3*4*5*6 = 360 does not contain the digit 2, while 1*2*3*4 = 24 and 2*3*4*5 = 120 do.
%p A360587 f:= proc(n) local k,t;
%p A360587 t:= n!;
%p A360587 for k from 1 to 100000 do
%p A360587    if not member(2,convert(t,base,10)) then return k fi;
%p A360587    t:= t*(n+k)/k;
%p A360587 od:
%p A360587 -1
%p A360587 end proc:
%p A360587 map(f, [$1..32]);
%Y A360587 Cf. A173333.
%K A360587 nonn,base,more
%O A360587 1,2
%A A360587 _Robert Israel_, Feb 12 2023