A011020 -id:A011020 - cp's OEIS frontend

A281143 Decimal expansion of 10!^(1/10).

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

Offset: 1

Robert G. Wilson v, Jan 15 2017

Base b such that log_b 10! = 10.

Inspired by the idea of utilizing the log scaled to 10! being 10, i.e., log_b 10! = 10, therefore b = 2^(4/5)*3^(2/5)*5^(1/5)*7^(1/10).

			4.52872868811676476220330933719550879349863167608939046288611476046926255...

Cf. A002193, A005486, A005534, A011020, A011092, A011094, A011101.

RealDigits[2^(4/5) 3^(2/5) 5^(1/5) 7^(1/10), 10, 111][[1]] (* or *)
RealDigits[Solve[Log[b, 10!] == 10, b][[1, 1, 2]], 10, 105][[1]]

Equals A011101 * A011094 * A005534 * A011092.

A382197 Decimal expansion of 24^(1/6).

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, Mar 18 2025

			1.69838132956495278491256452465974936020350009...

Jean-Paul Allouche, Jeffrey Shallit, and Manon Stipulanti, Combinatorics on words and generating Dirichlet series of automatic sequences, arXiv:2401.13524 [math.CO], 2025. See Theorem 10 at p. 20.

Cf. A002193, A010480, A010596, A011020, A011109, A246708.

Mathematica
```
RealDigits[24^(1/6),10,100][[1]]
```

Equals A002193*A246708.

cp's OEIS Frontend

A281143 Decimal expansion of 10!^(1/10).

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