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A008565 Digits of powers of 4.

%I A008565 #25 Mar 23 2025 03:57:08
%S A008565 1,4,1,6,6,4,2,5,6,1,0,2,4,4,0,9,6,1,6,3,8,4,6,5,5,3,6,2,6,2,1,4,4,1,
%T A008565 0,4,8,5,7,6,4,1,9,4,3,0,4,1,6,7,7,7,2,1,6,6,7,1,0,8,8,6,4,2,6,8,4,3,
%U A008565 5,4,5,6,1,0,7,3,7,4,1,8,2,4,4,2,9,4,9,6,7,2,9,6,1,7,1,7,9,8,6,9,1,8,4
%N A008565 Digits of powers of 4.
%C A008565 Irregular table with row length sequence A210434. - _Jason Kimberley_, Nov 26 2012
%C A008565 The constant whose decimal expansion is this sequence is irrational (Mahler, 1981). - _Amiram Eldar_, Mar 23 2025
%H A008565 Robert Israel, <a href="/A008565/b008565.txt">Table of n, a(n) for n = 0..10008</a> (rows 0 to 181, flattened)
%H A008565 Kurt Mahler, <a href="https://doi.org/10.1016/0022-314X(81)90010-X">On some irrational decimal fractions</a>, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.
%e A008565 Triangle begins:
%e A008565   1;
%e A008565   4;
%e A008565   1, 6;
%e A008565   6, 4;
%e A008565   2, 5, 6;
%e A008565   1, 0, 2, 4;
%e A008565   4, 0, 9, 6;
%e A008565   1, 6, 3, 8, 4;
%e A008565   6, 5, 5, 3, 6;
%e A008565   2, 6, 2, 1, 4, 4;
%e A008565   1, 0, 4, 8, 5, 7, 6;
%e A008565   ...
%p A008565 R:= 1: t:= 1: count:= 1:
%p A008565 while count < 100 do
%p A008565   t:= 4*t; L:= convert(t,base,10);
%p A008565   count:= count+nops(L);
%p A008565   R:= R, op(ListTools:-Reverse(L));
%p A008565 od:
%p A008565 R; # _Robert Israel_, May 05 2020
%t A008565 Table[IntegerDigits[4^i],{i,0,17}]//Flatten (* _Stefano Spezia_, Aug 06 2024 *)
%Y A008565 Cf. A000302 (powers of 4), A210434.
%Y A008565 Last elements of rows give A168428.
%Y A008565 Cf. A000455, A008564, A008566, A008567, A008568, A008569, A008570, A008571, A008572, A008573, A010054.
%K A008565 nonn,base,easy,tabf
%O A008565 0,2
%A A008565 _N. J. A. Sloane_