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A056992 Digital roots of square numbers A000290. 17
1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Cyclic with a period of nine. Note that (7, 9, 4, 1, 9, 1, 4, 9, 7) is palindromic.
a(n) is also the decimal expansion of 499264730/333333333. - Enrique Pérez Herrero, Jul 28 2009
a(n) is also the digital root of the Wonderful Demlo number A002477(n). - Enrique Pérez Herrero, Dec 20 2009
First comment above by Enrique Pérez Herrero and his formula below together give the following identity: 1+Sum_{n>=2}(1+9*((n^2-1)/9-floor((n^2-1)/9)))/10^(n-1) = 499264730/333333333 = 1.49779419149779419149779419... - Alexander R. Povolotsky, Jun 14 201
LINKS
Eric Weisstein's World of Mathematics, Square Number.
FORMULA
a(n) = 1+9*{(n^2-1)/9} , where the symbol {} means fractional part. - Enrique Pérez Herrero, Dec 20 2009
a(n) = 3(1 + cos(2n*Pi/3) + cos(4n*Pi/3)) + mod(3n^4+3n^6+4n^8,9). - Ant King, Oct 07 2009
G.f.: x (1+4x+9x^2+7x^3+7x^4+9x^5+4x^6+x^7+9x^8)/((1-x)(1+x+x^2)(1+x^3+x^6)). - Ant King, Oct 20 2009
Also a(n) = A010888(A057147(n)). - Reinhard Zumkeller, Mar 19 2014
MATHEMATICA
DigitalRoot[n_Integer?NonNegative] := 1 + 9*FractionalPart[(n - 1)/9] A056992[n_]:=DigitalRoot[n^2] (* Enrique Pérez Herrero, Dec 20 2009 *)
Table[FixedPoint[Total[IntegerDigits[#]]&, n^2], {n, 90}] (* Zak Seidov, Jun 13 2015 *)
PadRight[{}, 120, {1, 4, 9, 7, 7, 9, 4, 1, 9}] (* Harvey P. Dale, Apr 16 2022 *)
PROG
(Haskell)
a056992 = a010888 . a000290 -- Reinhard Zumkeller, Mar 19 2014
CROSSREFS
Sequence in context: A296425 A335089 A306004 * A339023 A169908 A004159
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)