A008565 Digits of powers of 4.

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, 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, 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy
• tabf

Comments

Irregular table with row length sequence A210434. - Jason Kimberley, Nov 26 2012

The constant whose decimal expansion is this sequence is irrational (Mahler, 1981). - Amiram Eldar, Mar 23 2025

Examples

			Triangle begins:
  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, 0, 4, 8, 5, 7, 6;
  ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10008 (rows 0 to 181, flattened)
• Kurt Mahler, On some irrational decimal fractions, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.

Crossrefs

Cf. A000302 (powers of 4), A210434.

Last elements of rows give A168428.

Cf. A000455, A008564, A008566, A008567, A008568, A008569, A008570, A008571, A008572, A008573, A010054.

Programs

Maple

R:= 1: t:= 1: count:= 1:
while count < 100 do
  t:= 4*t; L:= convert(t,base,10);
  count:= count+nops(L);
  R:= R, op(ListTools:-Reverse(L));
od:
R; # Robert Israel, May 05 2020

Mathematica

Table[IntegerDigits[4^i],{i,0,17}]//Flatten (* Stefano Spezia, Aug 06 2024 *)