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A056991
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Numbers with digital root 1, 4, 7 or 9.
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6
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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
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OFFSET
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1,2
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COMMENTS
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All squares are members.
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]
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LINKS
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Table of n, a(n) for n=1..63.
Eric Weisstein's World of Mathematics, Square Number
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FORMULA
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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)=a(n-4)+9. O.g.f.: x(2x+1)(x^2+x+1)/((-1+x)^2*(1+x)(x^2+1)). R. J. Mathar Apr 30 2008
a(n) = 3*(n-floor(n/4)) - (3-I^n-(-I)^n-(-1)^n)/2 [From Gary Detlefs, Mar 19 2010]
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MAPLE
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seq( 3*(n-floor(n/4)) - (3-I^n-(-I)^n-(-1)^n)/2, n=1..63); [From Gary Detlefs, Mar 19 2010]
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PROG
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(PARI) forstep(n=1, 1e3, [3, 3, 2, 2], print1(n", ")) \\ Charles R Greathouse IV, Sep 21 2012
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CROSSREFS
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Cf. A000290, A056992.
Sequence in context: A153053 A045752 A010380 * A010389 A010415 A010442
Adjacent sequences: A056988 A056989 A056990 * A056992 A056993 A056994
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KEYWORD
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nonn,base
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar
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STATUS
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approved
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