A390487 Numbers k with the property that k is the next lexicographically earliest number that cannot be expressed as a linear sum of the squares of preceding terms of the sequence with coefficients of 0, +1 or -1, with a(1)=1.

1, 2, 6, 7, 11, 15, 21, 25, 61, 106, 142, 155, 515, 551, 36208, 36384, 40021, 40713, 51765, 56463, 56814, 56859, 154582, 154631, 158303, 158352, 6153954

Offset

1,2

Comments

We can classify all numbers as 'reachable' or 'unreachable' as the linear sum of previous term squares, this sequence is then the list of 'unreachable' terms.

Links

Table of n, a(n) for n=1..27.

Sean A. Irvine, Java program (github)

Example

106 is unreachable, but 107 = -1^2 + 6^2 - 7^2 + 11^2.

Prog

(Python)
from itertools import islice
def A390487_gen(): # generator of terms
    bset, a = {0, 1}, 2
    yield 1
    while True:
        yield a
        bset = set().union(*({d, d+a**2, abs(d-a**2)} for d in bset))
        a += 1
        while a in bset:
            a += 1
A390487_list = list(islice(A390487_gen(), 15)) # Chai Wah Wu, Nov 13 2025

Crossrefs

Sums of j squares: A000290 (j=1), A000404 (j=2), A000408 (j=3), A000414 (j=4), A047700 (j=5).

Sum of all squares less than n: A000330.

Sequence in context: A214991 A286995 A088227 * A231500 A174000 A241720

Adjacent sequences: A390484 A390485 A390486 * A390488 A390489 A390490

Keyword

nonn,more

Author

Benjamin W P Cornish, Nov 07 2025

Extensions

a(20)-a(27) from Sean A. Irvine, Nov 12 2025

Status

approved