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

31, 3141, 3141592, 314159265, 31415926535897932384626433

Offset: 1

Author

Michel Lagneau, Aug 18 2016

Keywords

• nonn
• base

Comments

Members of A011545.

a(6)= 3141592653...647093 contains 123 digits;

a(7)= 3141592653...128475 contains 226 digits;

a(8)= 3141592653...786783 contains 238 digits;

a(9)= 3141592653...789259 contains 357 digits;

a(10)= 3141592653...892590 contains 358 digits;

a(11)= 3141592653...261179 contains 441 digits.

The corresponding partial sums are 4, 9, 25, 36, 121,...(subsequence of A046974).

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,...

The primes in b(n) are 2, 3, 5, 11, 89, 101, 173, 197, 227,...

The squares in b(n) are 100, 121, 144, 196, 256, 289, 324, 729, 784,..

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..17

Crossrefs

Cf. A000796, A011545, A046974.

Programs

Mathematica

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}]
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 *)