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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.
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%I #9 Jul 22 2014 10:27:34

%S 2,23,87,157,1523,3445551,26620870,30512347,72713283,344661698,

%T 1129330411,3886591581,5085084202,11916345303,15510679381

%N 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.

%C 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.

%C The second-half numbers:

%C 1 1

%C 2 97932384626

%C 3 99375105820974944592..

%C 4 99862803482534211706..

%C 5 99999983729780499510..

%C 6 99999993176688420006..

%C 7 10000000420467135547..

%C 8 99999998414267344764..

%C 9 99999999542282360035..

%C 10 10000000012202360559..

%C 11 99999999941927584272..

%C 12 99999999948261395946..

%C 13 10000000002413899137..

%C 14 99999999975954453917..

%C 15 99999999988383727123..

%e 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.

%Y Cf. A000796, A048940, A193940.

%K nonn,base

%O 1,1

%A _Eric Angelini_ and _Hans Havermann_, Jul 18 2014

%E a(12)-a(15) from _Hans Havermann_, Jul 19 2014