A074755 Number of n-digit non-leading-zero trimorphic numbers (m such that m^3 ends in m).

5, 7, 13, 11, 11, 13, 12, 13, 12, 13, 13, 11, 10, 12, 12, 13, 12, 12, 12, 11, 13, 12, 12, 10, 10, 13, 13, 13, 11, 13, 12, 10, 10, 11, 11, 13, 13, 10, 13, 11, 13, 12, 13, 12, 12, 13, 12, 12, 12, 12, 12, 11, 10, 10, 13, 13, 13, 13, 13, 13, 11, 13, 12, 10, 11, 11, 13

Offset: 1

Author

David W. Wilson, Sep 28 2002

Keywords

• nonn
• base

Comments

For n >= 3, I can show 8 <= a(n) <= 13 and I highly suspect that 10 <= a(n) <= 13 from empirical evidence.

If n >= 3, there are 15 integers 0 <= x < 10^n with x == 0, 1 or -1 mod 5^n and x == 0, 1, -1, 2^(n-1)-1 or 2^(n-1)+1 mod 2^n, and a(n) is the number of these that are >= 10^(n-1). - Robert Israel, Jul 07 2014

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A033819.

Programs

Maple

f:= n ->
  nops(select(`>=`,{seq(seq(chrem([a,b],[2^n,5^n]),a={0,1,2^(n-1)-1,2^(n-1)+1,-1}),b={0,1,-1})},10^(n-1))):
seq(f(n), n=1..100); # Robert Israel, Jul 07 2014