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A056991 Numbers with digital root 1, 4, 7 or 9. 11
1, 4, 7, 9, 10, 13, 16, 18, 19, 22, 25, 27, 28, 31, 34, 36, 37, 40, 43, 45, 46, 49, 52, 54, 55, 58, 61, 63, 64, 67, 70, 72, 73, 76, 79, 81, 82, 85, 88, 90, 91, 94, 97, 99, 100, 103, 106, 108, 109, 112, 115, 117, 118, 121, 124, 126, 127, 130, 133, 135, 136, 139, 142 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All squares are members (see A070433).

May also be defined as: possible sums of digits of squares. - Zak Seidov, Feb 11 2008

First differences are periodic: 3, 3, 2, 1, 3, 3, 2, 1, 3, 3, 2, 1, 3, 3, 2, 1, 3, 3, 2, 1, 3, 3, 2, 1, 3, 3, 2, 1, ... - Zak Seidov, Feb 11 2008

Minimal n with corresponding sum-of-digits(n^2) are: 1, 2, 4, 3, 8, 7, 13, 24, 17, 43, 67, 63, 134, 83, 167, 264, 314, 313, 707, 1374, 836, 1667, 2236, 3114, 4472, 6833, 8167, 8937, 16667, 21886, 29614, 60663, 41833, 74833, 89437, 94863, 134164, 191833.

a(n) is the set of all m such that 9k+m can be a perfect square.(quadratic residues of 9 including the trivial case of 0) [From Gary Detlefs, Mar 19 2010]

REFERENCES

H. I. Okagbue, M. O. Adamu, S. A. Iyase, A. A. Opanuga, Sequence of Integers Generated by Summing the Digits of their Squares, Indian Journal of Science and Technology, Vol 8(15), DOI: 10.17485/ijst/2015/v8i15/69912, July 2015

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..22222

Eric Weisstein's World of Mathematics, Square Number

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

O.g.f.: x(2x+1)(x^2+x+1)/[(-1+x)^2 (x+1)(x^2+1)] . a(n)=a(n-4)+9 . - R. J. Mathar, Feb 14 2008

a(n) = Sum_{k=0..n}(1/8)*{5*(k mod 4)+5*[(k+1) mod 4]+3*[(k+2) mod 4]-[(k+3) mod 4]}, with n>=0. - Paolo P. Lava, Feb 15 2008

a(n) = 3*(n-floor(n/4)) - (3-I^n-(-I)^n-(-1)^n)/2. [From Gary Detlefs, Mar 19 2010]

MAPLE

seq( 3*(n-floor(n/4)) - (3-I^n-(-I)^n-(-1)^n)/2, n=1..63); # [From Gary Detlefs, Mar 19 2010]

MATHEMATICA

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 4, 7, 9, 10}, 70] (* Harvey P. Dale, Aug 29 2015 *)

PROG

(PARI) forstep(n=1, 1e3, [3, 3, 2, 1], print1(n", ")) \\ Charles R Greathouse IV, Sep 21 2012

CROSSREFS

Cf. A000290, A056992, A070433.

For complement see A268226.

Sequence in context: A045752 A266410 A010380 * A242660 A010389 A010415

Adjacent sequences:  A056988 A056989 A056990 * A056992 A056993 A056994

KEYWORD

nonn,base,easy

AUTHOR

Eric W. Weisstein

EXTENSIONS

Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar

STATUS

approved

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Last modified December 7 11:42 EST 2016. Contains 278874 sequences.