A355622 a(n) is the n-digit positive number with no trailing zeros and coprime to its digital reversal R(a(n)) at which abs(a(n)/R(a(n))-Pi) is minimized.

1, 92, 581, 5471, 52861, 998713, 7774742, 93630892, 422334431, 9190135292, 45425395441, 472539314051, 5784475521481, 49371008251751, 939253175379892, 9265811239939492, 52949745472445861, 952186420153090303, 9836241210282790313, 36386277546811128511, 442327789252803797041

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. A355623 (denominator 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[k/FromDigits[Reverse[IntegerDigits[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