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Numbers k such that k*(k+1) does not contain the digit 2.
1

%I #31 Feb 16 2023 19:40:44

%S 2,5,7,9,10,12,17,19,22,24,25,27,29,30,32,34,37,39,40,42,44,55,57,59,

%T 60,62,64,67,69,70,74,75,77,80,82,84,85,87,89,90,92,94,97,99,100,102,

%U 105,107,109,114,115,117,122,124,125,129,130,132,134,135,137,139,140,174,175,177,182,184,185

%N Numbers k such that k*(k+1) does not contain the digit 2.

%C All terms == 0, 2, 4, 5, 7, or 9 (mod 10).

%H Robert Israel, <a href="/A360411/b360411.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 9 is a term because 9*10 = 90 does not contain the digit 2.

%p remove(t -> member(2,convert(t*(t+1),base,10)), [$1..1000]);

%K nonn,base

%O 1,1

%A _Robert Israel_, Feb 12 2023