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

Author

Reinhard Zumkeller, Jul 20 2008

Keywords

• nonn

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.