A008570 -id:A008570 - cp's OEIS frontend

A000455 Digits of powers of 2.

1, 2, 4, 8, 1, 6, 3, 2, 6, 4, 1, 2, 8, 2, 5, 6, 5, 1, 2, 1, 0, 2, 4, 2, 0, 4, 8, 4, 0, 9, 6, 8, 1, 9, 2, 1, 6, 3, 8, 4, 3, 2, 7, 6, 8, 6, 5, 5, 3, 6, 1, 3, 1, 0, 7, 2, 2, 6, 2, 1, 4, 4, 5, 2, 4, 2, 8, 8, 1, 0, 4, 8, 5, 7, 6, 2, 0, 9, 7, 1, 5, 2

Offset: 0

N. J. A. Sloane; entry revised by N. J. A. Sloane, Jun 10 2012

The number 0.a(0)a(1)a(2)...=0.124816... is a rich (or disjunctive) number. - Robert FERREOL, Apr 01 2020

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

David Gale, Tracking the Automatic ANT And Other Mathematical Explorations, 1998, pp. 42-43.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane, Table of n, a(n) for n = 0..9999
Archimedeans, The Problems Drive, Eureka, Vol. 11 (1949), p. 10, problem (5) B.
Kurt Mahler, On some irrational decimal fractions, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.

Cf. A000079.

Cf. A008564, A008565, A008566, A008567, A008568, A008569, A008570, A008571, A008572, A008573, A010054.

2^Range[0, 25] // IntegerDigits // Flatten (* Jean-François Alcover, Feb 08 2016 *)

(List.fill(32)(2: BigInt)).scanLeft(1: BigInt)( * ).map(.toString.toCharArray).flatten.map(.toInt - 48) // Alonso del Arte, Mar 28 2020

A008565 Digits of powers of 4.

Original entry on oeis.org

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

N. J. A. Sloane

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

			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;
  ...

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.

Cf. A000302 (powers of 4), A210434.
Last elements of rows give A168428.
Cf. A000455, A008564, A008566, A008567, A008568, A008569, A008570, A008571, A008572, A008573, A010054.

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

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

A008566 Digits of powers of 5.

Original entry on oeis.org

1, 5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3, 9, 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8, 1, 2, 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1, 0, 3, 5, 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8, 7, 8

Offset: 0

N. J. A. Sloane

Irregular table with row length sequence A210435. - Jason Kimberley, Nov 26 2012

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

			Triangle begins:
  1;
  5;
  2, 5;
  1, 2, 5;
  6, 2, 5;
  3, 1, 2, 5;
  1, 5, 6, 2, 5;
  7, 8, 1, 2, 5,
  3, 9, 0, 6, 2, 5;
  ...

Seiichi Manyama, Rows n = 0..100, flattened
Kurt Mahler, On some irrational decimal fractions, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.

Cf. A000351, A210435.

Cf. A000455, A008564, A008565, A008567, A008568, A008569, A008570, A008571, A008572, A008573, A010054.

Flatten[IntegerDigits/@(5^Range[0,20])] (* Harvey P. Dale, Jan 18 2012 *)

A008567 Digits of powers of 6.

Original entry on oeis.org

1, 6, 3, 6, 2, 1, 6, 1, 2, 9, 6, 7, 7, 7, 6, 4, 6, 6, 5, 6, 2, 7, 9, 9, 3, 6, 1, 6, 7, 9, 6, 1, 6, 1, 0, 0, 7, 7, 6, 9, 6, 6, 0, 4, 6, 6, 1, 7, 6, 3, 6, 2, 7, 9, 7, 0, 5, 6, 2, 1, 7, 6, 7, 8, 2, 3, 3, 6, 1, 3, 0, 6, 0, 6, 9, 4, 0, 1, 6, 7, 8, 3, 6, 4, 1, 6, 4, 0, 9, 6, 4, 7, 0, 1, 8, 4, 9, 8, 4

Offset: 0

N. J. A. Sloane

Irregular table with row length sequence A210436. - Jason Kimberley, Nov 26 2012

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

			Triangle begins:
  1;
  6;
  3, 6;
  2, 1, 6;
  1, 2, 9, 6;
  7, 7, 7, 6;
  4, 6, 6, 5, 6;
  2, 7, 9, 9, 3, 6;
  1, 6, 7, 9, 6, 1, 6;
  1, 0, 0, 7, 7, 6, 9, 6;
  ...

Seiichi Manyama, Rows n = 0..100, flattened
Kurt Mahler, On some irrational decimal fractions, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.

Cf. A000400, A210436.

Cf. A000455, A008564, A008565, A008566, A008568, A008569, A008570, A008571, A008572, A008573, A010054.

A008568 Digits of powers of 7.

Original entry on oeis.org

1, 7, 4, 9, 3, 4, 3, 2, 4, 0, 1, 1, 6, 8, 0, 7, 1, 1, 7, 6, 4, 9, 8, 2, 3, 5, 4, 3, 5, 7, 6, 4, 8, 0, 1, 4, 0, 3, 5, 3, 6, 0, 7, 2, 8, 2, 4, 7, 5, 2, 4, 9, 1, 9, 7, 7, 3, 2, 6, 7, 4, 3, 1, 3, 8, 4, 1, 2, 8, 7, 2, 0, 1, 9, 6, 8, 8, 9, 0, 1, 0, 4, 0, 7, 6, 7, 8, 2, 2, 3, 0, 7, 2, 8, 4, 9, 4, 7, 4

Offset: 0

N. J. A. Sloane

Irregular table with row length sequence A210062. - Jason Kimberley, Nov 26 2012

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

			Triangle begins:
  1;
  7;
  4, 9;
  3, 4, 3;
  2, 4, 0, 1;
  1, 6, 8, 0, 7;
  1, 1, 7, 6, 4, 9;
  8, 2, 3, 5, 4, 3;
  ...

Seiichi Manyama, Rows n = 0..100, flattened
Kurt Mahler, On some irrational decimal fractions, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.

Cf. A000420, A210062.

Cf. A000455, A008564, A008565, A008566, A008567, A008569, A008570, A008571, A008572, A008573, A010054.

Flatten[IntegerDigits[7^Range[0,20]]]  (* Harvey P. Dale, Mar 03 2011 *)

A008571 Digits of powers of 11.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 6, 1, 0, 5, 1, 1, 7, 7, 1, 5, 6, 1, 1, 9, 4, 8, 7, 1, 7, 1, 2, 1, 4, 3, 5, 8, 8, 8, 1, 2, 3, 5, 7, 9, 4, 7, 6, 9, 1, 2, 5, 9, 3, 7, 4, 2, 4, 6, 0, 1, 2, 8, 5, 3, 1, 1, 6, 7, 0, 6, 1, 1, 3, 1, 3, 8, 4, 2, 8, 3, 7, 6, 7, 2, 1, 3, 4, 5, 2, 2, 7, 1, 2

Offset: 0

N. J. A. Sloane

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

			Triangle begins:
  1;
  1, 1;
  1, 2, 1;
  1, 3, 3, 1;
  1, 4, 6, 4, 1;
  1, 6, 1, 0, 5, 1;
  1, 7, 7, 1, 5, 6, 1;
  1, 9, 4, 8, 7, 1, 7, 1;
  2, 1, 4, 3, 5, 8, 8, 8, 1;
  ...

Seiichi Manyama, Rows n = 0..100, flattened
Kurt Mahler, On some irrational decimal fractions, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.

Cf. A001020, A348553.

Cf. A000455, A008564, A008565, A008566, A008567, A008568, A008569, A008570, A008572, A008573, A010054.

IntegerDigits[11^Range[0,20]]//Flatten (* Harvey P. Dale, Aug 26 2025 *)

A008564 Digits of powers of 3.

Original entry on oeis.org

1, 3, 9, 2, 7, 8, 1, 2, 4, 3, 7, 2, 9, 2, 1, 8, 7, 6, 5, 6, 1, 1, 9, 6, 8, 3, 5, 9, 0, 4, 9, 1, 7, 7, 1, 4, 7, 5, 3, 1, 4, 4, 1, 1, 5, 9, 4, 3, 2, 3, 4, 7, 8, 2, 9, 6, 9, 1, 4, 3, 4, 8, 9, 0, 7, 4, 3, 0, 4, 6, 7, 2, 1, 1, 2, 9, 1, 4, 0, 1, 6, 3, 3, 8, 7, 4, 2, 0, 4, 8, 9, 1, 1, 6, 2, 2, 6, 1, 4, 6, 7, 3

Offset: 0

N. J. A. Sloane

Irregular table with row length sequence A034888. - Jason Kimberley, Nov 26 2012

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

Muniru A Asiru, Table of n, a(n) for n = 0..5000
Kurt Mahler, On some irrational decimal fractions, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.

Cf. A000244, A034888.

Cf. A000455, A008565, A008566, A008567, A008568, A008569, A008570, A008571, A008572, A008573, A010054.

Flat(List([0..30],n->ListOfDigits(3^n))); # Muniru A Asiru, Sep 29 2018

Flatten[Table[IntegerDigits[3^n], {n, 0, 26}]] (* Alonso del Arte, Sep 29 2018 *)

A008569 Digits of powers of 8.

Original entry on oeis.org

1, 8, 6, 4, 5, 1, 2, 4, 0, 9, 6, 3, 2, 7, 6, 8, 2, 6, 2, 1, 4, 4, 2, 0, 9, 7, 1, 5, 2, 1, 6, 7, 7, 7, 2, 1, 6, 1, 3, 4, 2, 1, 7, 7, 2, 8, 1, 0, 7, 3, 7, 4, 1, 8, 2, 4, 8, 5, 8, 9, 9, 3, 4, 5, 9, 2, 6, 8, 7, 1, 9, 4, 7, 6, 7, 3, 6, 5, 4, 9, 7, 5, 5, 8, 1, 3, 8, 8, 8, 4, 3, 9, 8, 0, 4, 6, 5, 1, 1

Offset: 0

N. J. A. Sloane

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

			Triangle begins:
  1;
  8;
  6, 4;
  5, 1, 2;
  4, 0, 9, 6;
  3, 2, 7, 6, 8;
  2, 6, 2, 1, 4, 4;
  2, 0, 9, 7, 1, 5, 2;
  ...

Seiichi Manyama, Rows n = 0..100, flattened
Kurt Mahler, On some irrational decimal fractions, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.

Cf. A001018.

Cf. A000455, A008564, A008565, A008566, A008567, A008568, A008570, A008571, A008572, A008573, A010054.

IntegerDigits/@(8^Range[0,20])//Flatten (* Harvey P. Dale, Nov 14 2020 *)

A008572 Digits of powers of 12.

Original entry on oeis.org

1, 1, 2, 1, 4, 4, 1, 7, 2, 8, 2, 0, 7, 3, 6, 2, 4, 8, 8, 3, 2, 2, 9, 8, 5, 9, 8, 4, 3, 5, 8, 3, 1, 8, 0, 8, 4, 2, 9, 9, 8, 1, 6, 9, 6, 5, 1, 5, 9, 7, 8, 0, 3, 5, 2, 6, 1, 9, 1, 7, 3, 6, 4, 2, 2, 4, 7, 4, 3, 0, 0, 8, 3, 7, 0, 6, 8, 8, 8, 9, 1, 6, 1, 0, 0, 4, 4, 8, 2, 5, 6, 1, 0, 6, 9, 9, 3, 2, 0

Offset: 0

N. J. A. Sloane

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

			Triangle begins:
  1;
  1, 2;
  1, 4, 4;
  1, 7, 2, 8;
  2, 0, 7, 3, 6;
  2, 4, 8, 8, 3, 2;
  2, 9, 8, 5, 9, 8, 4;
  ...

Seiichi Manyama, Rows n = 0..100, flattened
Kurt Mahler, On some irrational decimal fractions, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.

Cf. A001021.

Cf. A000455, A008564, A008565, A008566, A008567, A008568, A008569, A008570, A008571, A008573, A010054.

Flatten[IntegerDigits/@(12^Range[0,15])] (* Harvey P. Dale, Dec 19 2011 *)

A008573 Digits of powers of 13.

Original entry on oeis.org

1, 1, 3, 1, 6, 9, 2, 1, 9, 7, 2, 8, 5, 6, 1, 3, 7, 1, 2, 9, 3, 4, 8, 2, 6, 8, 0, 9, 6, 2, 7, 4, 8, 5, 1, 7, 8, 1, 5, 7, 3, 0, 7, 2, 1, 1, 0, 6, 0, 4, 4, 9, 9, 3, 7, 3, 1, 3, 7, 8, 5, 8, 4, 9, 1, 8, 4, 9, 1, 7, 9, 2, 1, 6, 0, 3, 9, 4, 0, 3, 7, 2, 3, 2, 9, 8, 0, 8, 5, 1, 2, 2, 4, 8, 1, 3, 0, 2, 8

Offset: 0

N. J. A. Sloane

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

			Triangle begins:
  1;
  1, 3;
  1, 6, 9;
  2, 1, 9, 7;
  2, 8, 5, 6, 1;
  3, 7, 1, 2, 9, 3;
  4, 8, 2, 6, 8, 0, 9;
  ...

Seiichi Manyama, Rows n = 0..100, flattened
Kurt Mahler, On some irrational decimal fractions, Journal of Number Theory, Vol. 13, No. 2 (1981), pp. 268-269.

Cf. A001022.

Cf. A000455, A008564, A008565, A008566, A008567, A008568, A008569, A008570, A008571, A008572, A010054.

IntegerDigits/@(13^Range[0,20])//Flatten (* Harvey P. Dale, Oct 24 2017 *)

cp's OEIS Frontend

A000455 Digits of powers of 2.

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Mathematica

Scala

A008565 Digits of powers of 4.

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Maple

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A008566 Digits of powers of 5.

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A008567 Digits of powers of 6.

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A008568 Digits of powers of 7.

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A008571 Digits of powers of 11.

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Mathematica

A008564 Digits of powers of 3.

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GAP

Mathematica

A008569 Digits of powers of 8.

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