A348626 Greedy Egyptian fraction representation of 1 with square denominators.

2, 2, 2, 3, 3, 7, 12, 49, 340, 6153, 362275, 234314697, 4303312007019, 8064823505928103487, 21034270897045389505182033301, 13184627067084215135862894820778146400791573, 36011454158212923548860166370685543204871921069986403871775848271, 6820216143160044256325325882329406136711110111012515344838677137010956148075846307036940303634819

Offset

1,1

Comments

Greedy representation 1 = 1/a(1)^2 + 1/a(2)^2 + ... constructed similarly to Sylvester's sequence (A000058). Each a(n) is taken as small as possible keeping the remainder positive.

Links

Table of n, a(n) for n=1..18.

Prog

(PARI) s=1; for(n=1, 20, t=sqrtint(floor(1/s))+1; s-=1/t^2; print1(t, ", "));
(Python)
from math import isqrt
from fractions import Fraction
def A348626List():
    s = Fraction(1, 1)
    while True:
        t = isqrt(1 // s) + 1
        yield t
        s -= Fraction(1, t * t)
a = A348626List()
print([next(a) for _ in range(18)])  # Peter Luschny, Oct 26 2021

Crossrefs

Cf. A000058, A348625.

Sequence in context: A082861 A131704 A327746 * A124492 A338629 A057646

Adjacent sequences: A348623 A348624 A348625 * A348627 A348628 A348629

Keyword

nonn

Author

Max Alekseyev, Oct 25 2021

Status

approved