

A054791


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


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
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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)=(n1)^2


MATHEMATICA

a[n_] := a[n] = Which[r = Sqrt[n]; IntegerQ[r], a[r]^2, OddQ[n  Floor[r]^2], n+1, True, (n1)^2]; a[0]=0; a[1]=1; Table[a[n], {n, 0, 58}] (* JeanFrançois 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: A157020 A180253 A055225 * A167531 A062319 A178590
Adjacent sequences: A054788 A054789 A054790 * A054792 A054793 A054794


KEYWORD

nice,nonn


AUTHOR

Henry Bottomley, Apr 27 2000


STATUS

approved



