A245331 Number of truncated Pi decimal digits that yield record approximations to Pi when the concatenation of the first half of the digits is divided by the second half.

2, 23, 87, 157, 1523, 3445551, 26620870, 30512347, 72713283, 344661698, 1129330411, 3886591581, 5085084202, 11916345303, 15510679381

Offset: 1

Author

Eric Angelini and Hans Havermann, Jul 18 2014

Keywords

• nonn
• base

Comments

For odd terms, the number of digits in the first "half" is one more than in the second half. Even terms imply the second half begins with 1; odd terms, with 9.

The second-half numbers:

1 1

2 97932384626

3 99375105820974944592..

4 99862803482534211706..

5 99999983729780499510..

6 99999993176688420006..

7 10000000420467135547..

8 99999998414267344764..

9 99999999542282360035..

10 10000000012202360559..

11 99999999941927584272..

12 99999999948261395946..

13 10000000002413899137..

14 99999999975954453917..

15 99999999988383727123..

Examples

			a(1) is 2 because 3/1 (1+1 digits) provides the first approximation to Pi. a(2) is 23 because 314159265358/97932384626 (12+11 digits) provides the next better approximation.
		

Crossrefs

Cf. A000796, A048940, A193940.

Extensions

a(12)-a(15) from Hans Havermann, Jul 19 2014