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Number of integers m in [0..10^n-1] such that m has no digit in common with the last n digits of either m^2, m^3 or m^4.
3

%I #14 May 02 2015 10:47:41

%S 4,15,33,46,67,75,76,64,77,69,75,72,75,96,121,137,127,139,152,153,161,

%T 159,155,165,184,188,206,218,211,232,238,244,261,263,267,291,290,298,

%U 301,326,318,326,334,343,335,334,349,371,420,439,451,465,474,485,524

%N Number of integers m in [0..10^n-1] such that m has no digit in common with the last n digits of either m^2, m^3 or m^4.

%C Similar sequences with more than three powers have all their terms = 0.

%H Lars Blomberg, <a href="/A256715/b256715.txt">Table of n, a(n) for n = 1..300</a>

%e For n=2:

%e m = 88, m^2 = 7744, m^3 = 681472, m^4 = 59969536 and none of 44, 72, 36 has a digit in common with 88 so it is counted.

%e m = 89, m^2 = 7921, m^3 = 704969, m^4 = 62742241 and 69 has digit 9 in common with 89 so it is not counted.

%e For n=3:

%e m = 988, m^2 = 976144, m^3 = 964430272, m^4 = 952857108736 and none of 144, 272, 736 has a digit in common with 988 so it is counted.

%e m = 989, m^2 = 978121, m^3 = 967361669, m^4 = 956720690641 and 669 has digit 9 in common with 989 so it is not counted.

%Y Cf. A256713, A256714.

%K base,nonn

%O 1,1

%A _Lars Blomberg_, Apr 09 2015