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%I #14 Jun 14 2017 01:02:31
%S 7,159,270,308,745,758,1080,1227,7805
%N Nearest integer to 1/frac(Pi^A137994(n)), where frac(x) = x - floor(x).
%C Sequence A137994 could be defined as "least positive integer such that this one (without rounding) is increasing".
%C The term a(1)=7 is not surprising (3 + 1/7 = 3.14...) but it comes as a funny surprise that the next term, a(2)=159, matches the next 3 digits of Pi and a(3) just differs by 5 from the next 3 digits!
%o (PARI) default(realprecision,10^4); f=1; for(i=1,10^9, frac(Pi^i)<f || next; f=frac(Pi^i);print1(round(1/f),","))
%Y Cf. A137994, A001203, A001672, A137299, A138324.
%K nonn,more
%O 1,1
%A _M. F. Hasler_, inspired by _Leroy Quet_, Apr 05 2008
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