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Number of bases in which n requires at least one zero to be written.
3

%I #10 Dec 07 2019 12:18:24

%S 0,1,1,2,2,3,1,3,3,4,3,5,2,3,3,4,3,6,4,6,4,3,2,7,3,4,5,7,4,7,2,6,5,5,

%T 6,8,4,5,5,8,3,7,2,5,6,4,3,9,4,7,7,7,4,9,6,8,4,4,3,11,3,4,5,7,7,9,4,6,

%U 6,9,4,11,5,6,8,7,7,9,4,9,6,6,5,12,6,5,5,9,4,11,5,6,4,4,5,11,4,7,8,10,6

%N Number of bases in which n requires at least one zero to be written.

%H Eric M. Schmidt, <a href="/A077268/b077268.txt">Table of n, a(n) for n = 1..10000</a>

%e a(9)=3 since it requires zeros when written in bases 2, 3 or 9 (as 1001, 100 or 10 respectively).

%o (Sage) def A077268(n) : return sum(0 in n.digits(m) for m in range(2,n+1)) # _Eric M. Schmidt_, Jul 09 2014

%o (PARI) a(n) = sum(i=2, n, ! vecmin(digits(n, i))); \\ _Michel Marcus_, Jul 09 2014

%Y Cf. A033093, A062842, A077266, A077267.

%K base,nonn

%O 1,4

%A _Henry Bottomley_, Nov 01 2002