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%I #15 Jul 18 2021 12:49:54
%S 9,10,26,27,52,133,137,173,198,207,232,296,377,426,507,516,520,529,
%T 593,609,645,649,685,701,710,719,783,792,796,845,926,951,951,955,1019,
%U 1083,1099,1100,1181,1230,1231,1267,1348,1357,1438,1519,1528,1577,1602
%N Sum of squares of first n digits of Pi.
%C a(n) is prime for n = 7, 8, 19, 24, 26, ... a(n) is semiprime for n = 1, 2, 3, 6, 13, 18, 22, 23, ... a(n) is a perfect power for n = 1, 4, 18, ...
%H Harvey P. Dale, <a href="/A111033/b111033.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{i=1..n} A000796(i)^2.
%e a(1) = 3^2 = 9,
%e a(2) = 3^2 + 1^2 = 10,
%e a(3) = 3^2 + 1^2 + 4^2 = 26,
%e a(4) = 3^2 + 1^2 + 4^2 + 1^2 = 27,
%e a(5) = 3^2 + 1^2 + 4^2 + 1^2 + 5^2 = 52,
%e a(6) = 3^2 + 1^2 + 4^2 + 1^2 + 5^2 + 9^2 = 133,
%e a(7) = 3^2 + 1^2 + 4^2 + 1^2 + 5^2 + 9^2 + 2^2 = 137, which is prime.
%p Digits := 120 ;
%p A000796 := proc(n) floor(Pi*10^(n-1)) ; % mod 10 ; end proc:
%p A111033 := proc(n) add( A000796(i)^2,i=1..n) ; end proc:
%p seq(A111033(n),n=1..120) ; # _R. J. Mathar_, Dec 21 2010
%t Accumulate[RealDigits[Pi,10,50][[1]]^2] (* _Harvey P. Dale_, Jul 18 2021 *)
%o (Sage) A111033 = lambda n: sum(d**2 for d in floor(pi*10**(n-1)).digits()) # _D. S. McNeil_ Dec 22 2010
%Y Cf. A000796.
%K base,easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Oct 05 2005
%E More terms from _Vincenzo Librandi_, Dec 21 2010
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