A355623 a(n) is the n-digit positive number with no trailing zeros and coprime to its digital reversal R(a(n)) at which abs(R(a(n))/a(n)-Pi) is minimized.

1, 29, 185, 1745, 16825, 317899, 2474777, 29803639, 134433224, 2925310919, 14459352454, 150413935274, 1841255744875, 15715280017394, 298973571352939, 2949399321185629, 16854427454794925, 303090351024681259, 3130972820121426389, 11582111864577268363, 140797308252987723244

Offset: 1

Author

Stefano Spezia, Jul 10 2022

Keywords

• nonn
• base
• frac

Comments

a(n) and R(a(n)) have the same number of digits.

Petr Beckmann wrote that the fraction 92/29, corresponding to the second term of the sequence, appeared as value of Pi in a document written in A.D. 718.

Examples

			n              fraction    approximated value
-   -------------------    ------------------
1                     1    1
2                 92/29    3.1724137931034...
3               581/185    3.1405405405405...
4             5471/1745    3.1352435530086...
5           52861/16825    3.1418127786033...
6         998713/317899    3.1416047235128...
7       7774742/2474777    3.1415929596889...
8     93630892/29803639    3.1415926088757...
9   422334431/134433224    3.1415926690860...
...
		

References

• Petr Beckmann, A History of Pi, 3rd Ed., Boulder, Colorado: The Golem Press (1974): p. 27.

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..22

Crossrefs

Cf. A000796, A002485, A004086, A067251.

Cf. A355622 (numerator or digital reversal).

Programs

Mathematica

nmax=9; a={}; For[n=1, n<=nmax, n++, minim=Infinity; For[k=10^(n-1), k<=10^n-1, k++, If[(dist=Abs[FromDigits[Reverse[IntegerDigits[k]]]/k-Pi]) < minim && Last[IntegerDigits[k]]!=0 && GCD[k,FromDigits[Reverse[IntegerDigits[k]]]]==1, minim=dist; kmin=k]]; AppendTo[a, kmin]]; a

Extensions

a(10)-a(19) from Bert Dobbelaere, Jul 17 2022

a(20)-a(21) from Bert Dobbelaere, Sep 05 2022