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

1,2

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.

Links

Table of n, a(n) for n=1..30.

Example

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.

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]);

Crossrefs

Cf. A173333.

Sequence in context: A176120 A369595 A220621 * A058170 A238206 A127896

Adjacent sequences: A360584 A360585 A360586 * A360588 A360589 A360590

Keyword

nonn,base,more

Author

Robert Israel, Feb 12 2023

Status

approved