A215537 Lowest k such that k is representable as both the sum of n and of n+1 nonzero squares.

25, 17, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79

Offset

1,1

Links

Table of n, a(n) for n=1..70.

Example

25 = 5^2 = 3^2 + 4^2
17 = 4^2 + 1^2 = 3^2 + 2^2 + 2^2
12 = 2^2 + 2^2 + 2^2 = 3^2 + 1^2 + 1^2 + 1^2
after this just add 1^2 to both sides.

Maple

# true if a is representable as a sum of n squares, each square >= m^2.
isRepnSqrsMin := proc(a, n, m)
    local mpr ;
    if a < n*m^2 then
        return false;
    end if;
    if n = 1 then
        if a>= m^2 and issqr(a) then
            true;
        else
            false;
        end if;
    else
        for mpr from m to a do
            if a-mpr^2 < 1 then
                return false;
            elif procname(a-mpr^2, n-1, mpr) then
                return true;
            end if;
        end do:
    end if;
end proc:
# true if a is representable as a sum of n positive squares.
isRepnSqrs := proc(a, n)
    isRepnSqrsMin(a, n, 1) ;
end proc:
A215537 := proc(n)
    local k;
    for k from 1 do
        if isRepnSqrs(k, n) and isRepnSqrs(k, n+1) then
            return k;
        end if;
    end do:
end proc: # R. J. Mathar, Sep 11 2012

Crossrefs

Cf. A000290 (representable as sum of 1 square), A000404 (sum of 2 positive squares), A000408 (sum of 3 positive squares), A000414 (sum of 4 positive squares), A047700 (sum of 5 positive squares)

Sequence in context: A040602 A281335 A028937 * A104790 A291429 A334562

Adjacent sequences: A215534 A215535 A215536 * A215538 A215539 A215540

Keyword

nonn

Author

Jon Perry, Aug 15 2012

Status

approved