A054791 Earliest sequence with a(a(n)) = n^2.

0, 1, 3, 4, 9, 6, 25, 8, 49, 16, 11, 100, 13, 144, 15, 196, 81, 18, 289, 20, 361, 22, 441, 24, 529, 36, 27, 676, 29, 784, 31, 900, 33, 1024, 35, 1156, 625, 38, 1369, 40, 1521, 42, 1681, 44, 1849, 46, 2025, 48, 2209, 64, 51, 2500, 53, 2704, 55, 2916, 57, 3136, 59

Offset

0,3

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for sequences of the a(a(n)) = 2n family

Formula

if n is a square then a(n) = a(sqrt(n))^2, otherwise if the difference between n and the highest square less than n is odd then a(n) = n+1, otherwise a(n) = (n-1)^2.

Mathematica

a[n_] := a[n] = Which[r = Sqrt[n]; IntegerQ[r], a[r]^2, OddQ[n - Floor[r]^2], n+1, True, (n-1)^2]; a[0]=0; a[1]=1; Table[a[n], {n, 0, 58}] (* Jean-François Alcover, Aug 07 2012, after formula *)

Prog

(Haskell)
a054791 n = a054791_list `genericIndex` n
a054791_list = 0 : 1 : f 2 where
   f x | r ^ 2 == x  = a054791 r ^ 2 : f (x + 1)
       | odd (x - r) = x + 1         : f (x + 1)
       | otherwise   = (x - 1) ^ 2   : f (x + 1)
       where r = a000196 x
-- Reinhard Zumkeller, Oct 27 2013

Crossrefs

Cf. A002516.

Sequence in context: A180253 A264786 A055225 * A167531 A344195 A356541

Adjacent sequences: A054788 A054789 A054790 * A054792 A054793 A054794

Keyword

nice,nonn

Author

Henry Bottomley, Apr 27 2000

Status

approved