A360587 - OEIS

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

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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

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

KEYWORD

nonn,base,more

AUTHOR

STATUS

approved