login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056992 Digital roots of square numbers A000290. 12
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 Demlo numbers (A002477). - Enrique Pérez Herrero, Dec 20 2009

First above comment by Enrique Pérez Herrero and his formula below give together 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 2012

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

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) = (1/108)*{113*(n mod 9)-79*[(n+1) mod 9]+53*[(n+2) mod 9]+77*[(n+3) mod 9]-7*[(n+4) mod 9]+17*[(n+5) mod 9]+41*[(n+6) mod 9]-43*[(n+7) mod 9]-19*[(n+8) mod 9]}, with n>=0. - Paolo P. Lava, Aug 04 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 *)

PROG

(Haskell)

a056992 = a010888 . a000290  -- Reinhard Zumkeller, Mar 19 2014

CROSSREFS

Cf. A000290, A056991.

Sequence in context: A245670 A166923 A021205 * A169908 A004159 A092554

Adjacent sequences:  A056989 A056990 A056991 * A056993 A056994 A056995

KEYWORD

nonn,base,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified July 23 22:27 EDT 2017. Contains 289716 sequences.