A060956 -id:A060956 - cp's OEIS frontend

A364185 Leading digit of 11^n.

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

Offset: 0

Seiichi Manyama, Jul 15 2023

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A008952, A060956, A111395, A362871, A363093, A363249.

Cf. A000030, A001020, A008571.

a[n_] := IntegerDigits[11^n][[1]]; Array[a, 100, 0] (* Amiram Eldar, Jul 15 2023 *)

PARI
```
a(n) = digits(11^n)[1];
```

a(n) = A000030(A001020(n)).

A111395 First digit of powers of 5.

Original entry on oeis.org

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

Offset: 0

Almerio A. Castro (almerio.castro(AT)gmail.com), Nov 11 2005

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A008952, A060956.

Cf. A000030, A000351, A008566.

First[IntegerDigits[#]]&/@(5^Range[0,100]) (* Harvey P. Dale, Jan 13 2015 *)

a(n) = digits(5^n)[1]; \\ Michel Marcus, Jan 07 2014

a(n) = A000030(A000351(n)). - Seiichi Manyama, Jul 15 2023

a(0)=1 prepended, and more terms from Michel Marcus, Jan 07 2014

A363249 Leading digit of 9^n.

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Jul 15 2023

He, Xinwei; Hildebrand, A J; Li, Yuchen; Zhang, Yunyi, Complexity of Leading Digit Sequences, Discrete Mathematics and Theoretical Computer Science; 22 (2020), #14.

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A008952, A060956, A111395, A362871, A363093, A364185.

Cf. A000030, A001019, A008570.

a[n_] := IntegerDigits[9^n][[1]]; Array[a, 100, 0] (* Amiram Eldar, Jul 15 2023 *)

PARI
```
a(n) = digits(9^n)[1];
```

a(n) = A000030(A001019(n)).

a(n) = A060956(2*n).

A362871 Leading digit of 6^n.

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Jul 15 2023

Cf. A008952, A060956, A111395, A363093, A363249, A364185.

Cf. A000030, A000400, A008567.

a[n_] := IntegerDigits[6^n][[1]]; Array[a, 100, 0] (* Amiram Eldar, Jul 15 2023 *)

PARI
```
a(n) = digits(6^n)[1];
```

a(n) = A000030(A000400(n)).

A363093 Leading digit of 7^n.

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Jul 15 2023

Cf. A008952, A060956, A111395, A362871, A363249, A364185.

Cf. A000030, A000420, A001903, A008568.

a[n_] := IntegerDigits[7^n][[1]]; Array[a, 100, 0] (* Amiram Eldar, Jul 15 2023 *)

PARI
```
a(n) = digits(7^n)[1];
```

a(n) = A000030(A000420(n)).

A138028 The array of the most significant digit of n^k read by antidiagonals.

Original entry on oeis.org

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

Offset: 1

Robert G. Wilson v, Feb 10 2008

			n\k
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... .
1, 2, 4, 8, 1, 3, 6, 1, 2, 5, 1, 2, 4, 8, 1, 3, 6, 1, 2, 5, 1, ... .
1, 3, 9, 2, 8, 2, 7, 2, 6, 1, 5, 1, 5, 1, 4, 1, 4, 1, 3, 1, 3, ... .
1, 4, 1, 6, 2, 1, 4, 1, 6, 2, 1, 4, 1, 6, 2, 1, 4, 1, 6, 2, 1, ... .
1, 5, 2, 1, 6, 3, 1, 7, 3, 1, 9, 4, 2, 1, 6, 3, 1, 7, 3, 1, 9, ... .
1, 6, 3, 2, 1, 7, 4, 2, 1, 1, 6, 3, 2, 1, 7, 4, 2, 1, 1, 6, 3, ... .
1, 8, 6, 5, 4, 3, 2, 2, 1, 1, 1, 8, 6, 5, 4, 3, 2, 2, 1, 1, 1, ... .
1, 9, 8, 7, 6, 5, 5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, ... .
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... .
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, ... .
1, 1, 1, 1, 2, 2, 2, 3, 4, 5, 6, 7, 8, 1, 1, 1, 1, 2, 2, 3, 3, ... .
......................................................................

Cf. A008952, A060956, A138029, A061505.

f[n_, k_] := Quotient[n^k, 10^Floor[k*Log[10, n]]]; Table[f[ n - k, k], {n, 14}, {k, 0, n - 1}] // Flatten

A134468 Numbers n such that 2^n and 3^n have the same leading digit.

Original entry on oeis.org

0, 17, 28, 34, 40, 51, 57, 68, 80, 84, 85, 91, 97, 103, 107, 108, 114, 120, 125, 130, 142, 143, 147, 154, 159, 170, 176, 182, 187, 193, 199, 204, 206, 210, 216, 227, 233, 244, 250, 256, 260, 261, 267, 273, 278, 283, 284, 296, 301, 307, 318, 319, 323, 324, 330

Offset: 1

Lekraj Beedassy, Jan 20 2008

Cf. A008952, A060956.

A000030 := proc(n) op(-1, convert(n,base,10)) ; end: isA134468 := proc(n) if A000030(2^n) = A000030(3^n) then true ; else false; fi ; end: for n from 0 to 800 do if isA134468(n) then printf("%d, ",n) ; fi ; od: # R. J. Mathar, Jan 30 2008

Select[Range[0, 500], IntegerDigits[2^# ][[1]] == IntegerDigits[3^# ][[1]] &] (* Stefan Steinerberger, Jan 21 2008 *)

More terms from Stefan Steinerberger, Jan 21 2008

More terms from R. J. Mathar, Jan 30 2008

cp's OEIS Frontend

A364185 Leading digit of 11^n.

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A111395 First digit of powers of 5.

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A363249 Leading digit of 9^n.

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A362871 Leading digit of 6^n.

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Mathematica

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A363093 Leading digit of 7^n.

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A138028 The array of the most significant digit of n^k read by antidiagonals.

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A134468 Numbers n such that 2^n and 3^n have the same leading digit.

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Extensions