A111033 Sum of squares of first n digits of Pi.

9, 10, 26, 27, 52, 133, 137, 173, 198, 207, 232, 296, 377, 426, 507, 516, 520, 529, 593, 609, 645, 649, 685, 701, 710, 719, 783, 792, 796, 845, 926, 951, 951, 955, 1019, 1083, 1099, 1100, 1181, 1230, 1231, 1267, 1348, 1357, 1438, 1519, 1528, 1577, 1602

Offset

1,1

Comments

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, ...

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{i=1..n} A000796(i)^2.

Example

a(1) = 3^2 = 9,
a(2) = 3^2 + 1^2 = 10,
a(3) = 3^2 + 1^2 + 4^2 = 26,
a(4) = 3^2 + 1^2 + 4^2 + 1^2 = 27,
a(5) = 3^2 + 1^2 + 4^2 + 1^2 + 5^2 = 52,
a(6) = 3^2 + 1^2 + 4^2 + 1^2 + 5^2 + 9^2 = 133,
a(7) = 3^2 + 1^2 + 4^2 + 1^2 + 5^2 + 9^2 + 2^2 = 137, which is prime.

Maple

Digits := 120 ;
A000796 := proc(n) floor(Pi*10^(n-1)) ; % mod 10 ; end proc:
A111033 := proc(n) add( A000796(i)^2, i=1..n) ; end proc:
seq(A111033(n), n=1..120) ; # R. J. Mathar, Dec 21 2010

Mathematica

Accumulate[RealDigits[Pi, 10, 50][[1]]^2] (* Harvey P. Dale, Jul 18 2021 *)

Prog

(Sage) A111033 = lambda n: sum(d**2 for d in floor(pi*10**(n-1)).digits()) # D. S. McNeil Dec 22 2010

Crossrefs

Cf. A000796.

Sequence in context: A156787 A025043 A320728 * A123048 A189047 A041170

Adjacent sequences: A111030 A111031 A111032 * A111034 A111035 A111036

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Oct 05 2005

Extensions

More terms from Vincenzo Librandi, Dec 21 2010

Status

approved