A282888 Lexicographically earliest permutation p of the nonnegative integers such that Sum_{k=0..n} -(-1)^issquare(p(k))*p(k) is nonnegative for all n.

0, 1, 4, 2, 3, 9, 5, 16, 6, 7, 25, 8, 10, 11, 36, 12, 13, 14, 49, 15, 17, 64, 18, 19, 20, 21, 81, 22, 23, 24, 100, 26, 27, 28, 29, 121, 30, 31, 32, 33, 144, 34, 35, 37, 38, 169, 39, 40, 41, 42, 196, 43, 44, 45, 46, 225, 47, 48, 50, 51, 52, 256, 53, 54, 55, 56, 289, 57, 58, 59, 60, 61, 324, 62, 63, 65, 66, 67, 361, 68, 69, 70, 71, 72, 400, 73, 74, 75

Offset

0,3

Comments

In short: subtract nonsquares when you can, else add squares.

See A282887 for the partial (signed) sums.

A variant of A282840 (with partial sums A282886) and A282846 (corresponding to permutation A282864) and A282865; in the latter variants, "square" is replaced by "prime".

Links

Table of n, a(n) for n=0..87.

Example

Starting from a(0)=0 we add the square a(1)=1, and since we cannot subtract the nonsquare 2, we also add the next larger square a(2)=4. Then we can subtract nonsquares a(3)=2 and a(4)=3. Now we must add the square a(5)=9 before subtracting the nonsquare a(6)=5. Again we must add the next larger square a(7)=16 before subtracting the nonsquares a(8)=6 and a(9)=7. And so on.

Prog

(PARI) {print1(a=0); c=1; p=2; for(n=1, 199, old=a; if(a>=p, a-=p; while(issquare(p++), ), a+=c^2; c++); print1(", "abs(old-a))}

Crossrefs

Sequence in context: A351482 A143051 A297022 * A278101 A352416 A120240

Adjacent sequences: A282885 A282886 A282887 * A282889 A282890 A282891

Keyword

nonn

Author

M. F. Hasler and Eric Angelini, Feb 24 2017

Status

approved