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A061099 Squares with digital root 1. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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.
FORMULA
Conjecture: a(n)=(9*n+2)^2/4 for n even. a(n)=(9*n+7)^2/4 for n odd. G.f.: (1+63*x+34*x^2+63*x^3+x^4)/((1-x)^3*(1+x)^2). [Colin Barker, Apr 21 2012]
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
EXAMPLE
289 = 17^2, 2+8+9 = 19, 1+9 = 1, 1369 = 37^2, 1+3+6+9 = 19, 1+9 = 1.
PROG
(PARI) { b=0; for (n=0, 1000, until (s==1, b++; s=b^2; s-=9*(s\9)); write("b061099.txt", n, " ", b^2) ) } [Harry J. Smith, Jul 19 2009]
(PARI) SumD(x)= { s=0; while (x>9, s=s+x-10*(x\10); x=x\10); return(s + x) } { b=0; for (n=0, 1000, s=2; while (s!= 1, b++; s=b^2; while (s>9, s=SumD(s))); write("b061099.txt", n, " ", b^2) ) } [Harry J. Smith, Jul 17 2009]
(PARI) a(n)=(n\2*9-(-1)^n)^2 \\ Charles R Greathouse IV, Sep 20 2012
CROSSREFS
Squares of A056020.
Cf. A056991.
Sequence in context: A111730 A255990 A104022 * A118488 A088033 A303960
KEYWORD
nonn,base,easy
AUTHOR
Amarnath Murthy, Apr 19 2001
EXTENSIONS
More terms from Harry J. Smith, Jul 17 2009
STATUS
approved

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Last modified May 24 15:34 EDT 2024. Contains 372778 sequences. (Running on oeis4.)