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 A056991 Numbers with digital root 1, 4, 7 or 9. 20
 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). - Gary Detlefs, Mar 19 2010 From Klaus Purath, Feb 20 2023: (Start) The sum of digits of any term belongs to the sequence. Also the products of any terms belong to the sequence. This is the union of A017173, A017209, A017245 and A008591. Positive integers of the forms x^2 + (2*m+1)*x*y + (m^2+m-2)*y^2, for integers m. This sequence is closed under multiplication. (End) LINKS R. J. Mathar, Table of n, a(n) for n = 1..22222 H. I. Okagbue, M. O. Adamu, S. A. Iyase, and 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. Eric Weisstein's World of Mathematics, Square Number Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA From R. J. Mathar, Feb 14 2008: (Start) O.g.f.: x*(2x+1)*(x^2+x+1)/((-1+x)^2*(x+1)*(x^2+1)). a(n) = a(n-4) + 9. (End) a(n) = 3*(n - floor(n/4)) - (3 - i^n - (-i)^n - (-1)^n)/2, where i = sqrt(-1). - Gary Detlefs, Mar 19 2010 a(n) = a(n-1)+a(n-4)-a(n-5). - Wesley Ivan Hurt, May 27 2021 a(n) = 3*n - floor(n/4) - 2*floor((n+3)/4). - Ridouane Oudra, Jan 21 2024 E.g.f.: (cos(x) + (9*x - 1)*cosh(x) - 3*sin(x) + (9*x - 2)*sinh(x))/4. - Stefano Spezia, Feb 21 2024 MAPLE seq( 3*(n-floor(n/4)) - (3-I^n-(-I)^n-(-1)^n)/2, n=1..63); # 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, A008591, A017173, A017209, A017245, A056992, A070433. For complement see A268226. Sequence in context: A266410 A010380 A358348 * 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 August 8 12:42 EDT 2024. Contains 375021 sequences. (Running on oeis4.)