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

1,1

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

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

Crossrefs

Cf. A033819.

Sequence in context: A088897 A255233 A361708 * A354200 A002659 A357938

Adjacent sequences: A074752 A074753 A074754 * A074756 A074757 A074758

Keyword

nonn,base

Author

David W. Wilson, Sep 28 2002

Status

approved