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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 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). 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 Adjacent sequences: A061096 A061097 A061098 * A061100 A061101 A061102 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.)