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Each term k provides a value of (sum-of-digits of 5^k)/k that is closer to Pi than the previous value.
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%I #13 Apr 11 2021 04:19:48

%S 1,2,4,6,8,139,309,390,819,2868,6751,8045,9414,15008,15375,56839,

%T 84383,151286,307650,516962,533919,2021009

%N Each term k provides a value of (sum-of-digits of 5^k)/k that is closer to Pi than the previous value.

%H Hans Havermann, <a href="http://chesswanks.com/num/a119666search.jpg">Search for the next term</a>.

%t a = Infinity; fn = 1; p = N[Pi, 24]; Do[ fn = 5fn; b = N[ Abs[Pi - Plus @@ IntegerDigits@fn/n], 24]; If[b < a, a = b; Print@n], {n, 711000}] (* _Robert G. Wilson v_, Sep 08 2007 *)

%K base,fini,nonn,more

%O 1,2

%A _Hans Havermann_, Jul 29 2006, Jul 31 2006, Aug 05 2006