Search: id:A056991
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%I A056991
%S A056991 1,4,7,9,10,13,16,18,19,22,25,27,28,31,34,36,37,40,43,45,46,49,52,54,
%T A056991 55,58,61,63,64,67,70,72,73,76,79,81,82,85,88,90,91,94,97,99,100,103,
%U A056991 106,108,109,112,115,117,118,121,124,126,127,130,133,135,136,139,142
%N A056991 Numbers having digital root 1, 4, 7 or 9.
%C A056991 All squares are members.
%C A056991 May also be defined as: possible sums of digits of squares. - Zak Seidov 
               (zakseidov(AT)yahoo.com), Feb 11 2008
%C A056991 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 (zakseidov(AT)yahoo.com), 
               Feb 11 2008
%C A056991 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.
%H A056991 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SquareNumber.html">Link to a section of The World of Mathematics.</
               a>
%F A056991 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 (mathar(AT)strw.leidenuniv.nl), Feb 14 2008
%F A056991 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 (ppl(AT)spl.at), Feb 15 2008
%F A056991 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 (mathar(AT)strw.leidenuniv.nl) Apr 30 2008
%Y A056991 Cf. A000290, A056992.
%Y A056991 Sequence in context: A153053 A045752 A010380 this_sequence A010389 A010415 
               A010442
%Y A056991 Adjacent sequences: A056988 A056989 A056990 this_sequence A056992 A056993 
               A056994
%K A056991 nonn
%O A056991 1,2
%A A056991 Eric Weisstein (eric(AT)weisstein.com)
%E A056991 Edited by N. J. A. Sloane (njas(AT)research.att.com), May 16 2008 at 
               the suggestion of R. J. Mathar

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