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A276111 Decimal expansion of Pi truncated to numbers such that the partial sums of the decimal digits are perfect squares.

%I A276111 #16 May 24 2019 17:09:31
%S A276111 31,3141,3141592,314159265,31415926535897932384626433
%N A276111 Decimal expansion of Pi truncated to numbers such that the partial sums of the decimal digits are perfect squares.
%C A276111 Members of A011545.
%C A276111 a(6)= 3141592653...647093 contains 123 digits;
%C A276111 a(7)= 3141592653...128475 contains  226 digits;
%C A276111 a(8)= 3141592653...786783 contains 238 digits;
%C A276111 a(9)= 3141592653...789259 contains 357 digits;
%C A276111 a(10)= 3141592653...892590 contains 358 digits;
%C A276111 a(11)= 3141592653...261179 contains 441 digits.
%C A276111 The corresponding partial sums are 4, 9, 25, 36, 121,...(subsequence of A046974).
%C A276111 The corresponding square roots are in the following sequence b(n): 2, 3, 5, 6, 11, 24, 32, 33, 40, 44, 52, 62, 65, 66, 89, 100, 101, 110, 115, 116, 121, 135, 142, 144, 159, 161, 173, 177, 187, 190, 196, 197,...
%C A276111 The primes in b(n) are 2, 3, 5, 11, 89, 101, 173, 197, 227,...
%C A276111 The squares in b(n) are 100, 121, 144, 196, 256, 289, 324, 729, 784,..
%H A276111 Harvey P. Dale, <a href="/A276111/b276111.txt">Table of n, a(n) for n = 1..17</a>
%t A276111 L=Rest@FoldList[Plus,0,First@RealDigits[Pi,10,500]];Do[If[IntegerQ[Sqrt[L[[n]]]],Print[FromDigits[First@RealDigits[Pi,10,n]]]],{n,500}]
%t A276111 Module[{nn=50,pid,ac,po},pid=RealDigits[Pi,10,nn][[1]];ac=Accumulate[pid];po=Flatten[Position[ac,_?(IntegerQ[Sqrt[#]]&)]];FromDigits/@ Table[ Take[ pid,k],{k,po}]] (* _Harvey P. Dale_, May 24 2019 *)
%Y A276111 Cf. A000796, A011545, A046974.
%K A276111 nonn,base
%O A276111 1,1
%A A276111 _Michel Lagneau_, Aug 18 2016