A061099 Squares with digital root 1.
1, 64, 100, 289, 361, 676, 784, 1225, 1369, 1936, 2116, 2809, 3025, 3844, 4096, 5041, 5329, 6400, 6724, 7921, 8281, 9604, 10000, 11449, 11881, 13456, 13924, 15625, 16129, 17956, 18496, 20449, 21025, 23104, 23716, 25921, 26569, 28900, 29584
Offset: 1
Examples
289 = 17^2, 2+8+9 = 19, 1+9 = 1, 1369 = 37^2, 1+3+6+9 = 19, 1+9 = 1.
Links
- Harry J. Smith, Table of n, a(n) for n = 1..1001
- Amarnath Murthy & Charles Ashbacher, Fabricating a perfect square with a given valid digit sum, in Generalized Partitions and New Ideas On Number Theory and Smarandache Sequences, pp 154-156.
- Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
Programs
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PARI
a(n)=(n\2*9-(-1)^n)^2 \\ Charles R Greathouse IV, Sep 20 2012
Formula
From Colin Barker, Apr 21 2012: (Start)
a(n) = (9*n+2)^2/4 for n even; a(n)=(9*n+7)^2/4 for n odd.
G.f.: x*(1+63*x+34*x^2+63*x^3+x^4)/((1-x)^3*(1+x)^2). (End)
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5). - Wesley Ivan Hurt, Apr 21 2021
Extensions
More terms from Harry J. Smith, Jul 17 2009