login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
0
2, 23, 87, 157, 1523, 3445551, 26620870, 30512347, 72713283, 344661698, 1129330411, 3886591581, 5085084202, 11916345303, 15510679381
OFFSET
1,1
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..
EXAMPLE
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
KEYWORD
nonn,base
AUTHOR
Eric Angelini and Hans Havermann, Jul 18 2014
EXTENSIONS
a(12)-a(15) from Hans Havermann, Jul 19 2014
STATUS
approved