A070266 -id:A070266 - cp's OEIS frontend

A353243 Indices of records of A070266.

1, 2, 3, 4, 10, 11, 18, 27, 30, 32, 43, 69, 70, 264, 1409, 3027, 7471, 8946, 10576, 12595, 14034, 22849, 37124, 70083, 107868, 469850

Offset: 1

Amiram Eldar, Apr 08 2022

The corresponding record values are in A353244.

Cf. A001008, A002805, A070266, A091532, A353244.

m = Table[Max[ContinuedFraction[HarmonicNumber[n]]], {n, 1, 10^4}]; Map[FirstPosition[m, #][[1]] &, Union@FoldList[Max, m]]

from itertools import count, islice
from fractions import Fraction
from sympy.ntheory.continued_fraction import continued_fraction
def A353243_gen(): # generator of terms
    k, c = Fraction(), 0
    for n in count(1):
        k += Fraction(1,n)
        if c < (m := max(continued_fraction(k))):
            c = m
            yield n
A353243_list = list(islice(A353243_gen(),10)) # Chai Wah Wu, Apr 08 2022

A070266(a(n)) = A353244(n).

A353244 Record values of A070266.

Original entry on oeis.org

1, 2, 5, 12, 13, 50, 61, 68, 198, 1090, 1812, 2362, 32334, 1517757, 4150055, 8850618, 10459960, 34693154, 80385407, 277184250, 316848842, 426258508, 2150821469, 2901738400, 49091889811, 331178405563

Offset: 1

Amiram Eldar, Apr 08 2022

The corresponding indices are in A353243.

Cf. A001008, A002805, A070266, A091532, A353243.

Union @ FoldList[Max, Table[Max[ContinuedFraction[HarmonicNumber[n]]], {n, 1, 10^4}]]

from itertools import count, islice
from fractions import Fraction
from sympy.ntheory.continued_fraction import continued_fraction
def A353244_gen(): # generator of terms
    k, c = Fraction(), 0
    for n in count(1):
        k += Fraction(1,n)
        if c < (m := max(continued_fraction(k))):
            yield (c := m)
A353244_list = list(islice(A353244_gen(),10)) # Chai Wah Wu, Apr 08 2022

a(n) = A070266(A353243(n)).

A070267 Maximum element in the simple continued fraction expansion of e(n) = 1+1/2!+1/3!+...+1/n!.

Original entry on oeis.org

1, 2, 2, 3, 8, 5, 4, 14, 6, 29, 10, 16, 20, 18, 42, 59, 13, 14, 59, 35, 31, 184, 24, 65, 42, 64, 401, 71, 26, 24, 36, 31, 52, 187, 28, 41, 128, 177, 3041, 249, 315, 162, 118, 36, 101, 135, 86, 70, 194, 104, 274, 62, 2515, 305, 68, 59, 49, 88, 359, 280, 100, 702, 52

Offset: 1

Benoit Cloitre, May 09 2002

			The simple continued fraction expansion of e(10) is [1, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 11, 1, 1, 29, 1, 1, 2], hence a(10) = 29.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A061354, A061355, A069880, A070266.

Table[ Max[ ContinuedFraction[ Sum[1/i!, {i, 1, n}]]], {n, 1, 65}]

cp's OEIS Frontend

A353243 Indices of records of A070266.

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A353244 Record values of A070266.

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A070267 Maximum element in the simple continued fraction expansion of e(n) = 1+1/2!+1/3!+...+1/n!.

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