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.

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

Offset: 1

Author

Robert Israel, Feb 12 2023

Keywords

• nonn
• base
• more

Comments

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.

a(32) = 13.

Conjecture: a(n) = -1 for n = 31 and all n >= 33.

Examples

			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.
		

Crossrefs

Cf. A173333.

Programs

Maple

f:= proc(n) local k,t;
t:= n!;
for k from 1 to 100000 do
   if not member(2,convert(t,base,10)) then return k fi;
   t:= t*(n+k)/k;
od:
-1
end proc:
map(f, [$1..32]);