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A111033 Sum of squares of first n digits of Pi. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..49.

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

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

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Last modified June 14 00:35 EDT 2021. Contains 345016 sequences. (Running on oeis4.)