A143051 Smallest number not occurring earlier and smaller than the largest square so far, the next square if no such number exists.

0, 1, 4, 2, 3, 9, 5, 6, 7, 8, 16, 10, 11, 12, 13, 14, 15, 25, 17, 18, 19, 20, 21, 22, 23, 24, 36, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 49, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 64, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 81, 65, 66, 67, 68, 69, 70, 71

Offset

0,3

Comments

Permutation of the natural numbers, inverse: A143052;

A143053(n) = a(a(n));

a(A000290(n)) = A005563(n-1);

a(A002522(n)) = A000290(n+1);

for n>1: GCD(a(n^2),a(n^2+1)) = A050873(A000290(n),A002522(n)) =

A022998(n+1).

Links

Peter Kagey, Table of n, a(n) for n = 0..10000

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = if n=0 then 0 else if n=1+k^2 then n+2*k else n-1.

Crossrefs

Sequence in context: A026246 A321122 A351482 * A297022 A282888 A278101

Adjacent sequences: A143048 A143049 A143050 * A143052 A143053 A143054

Keyword

nonn

Author

Reinhard Zumkeller, Jul 20 2008

Status

approved