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

1,1

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

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 *)

Crossrefs

Cf. A000796, A011545, A046974.

Sequence in context: A377754 A217913 A174584 * A271070 A262926 A330398

Adjacent sequences: A276108 A276109 A276110 * A276112 A276113 A276114

Keyword

nonn,base

Author

Michel Lagneau, Aug 18 2016

Status

approved