A258252 -id:A258252 - cp's OEIS frontend

A258253 Putative inverse of A258252.

1, 2, 4, 5, 11, 3, 14, 15, 18, 8, 29, 6, 46, 9, 7, 47, 73, 17, 134, 35, 33, 26, 153, 16, 96, 27, 154, 34, 292, 12, 269, 185, 19, 85, 10, 49, 240, 86, 69, 21, 535, 13, 536, 64, 50, 271, 408, 48, 213, 114, 32, 63, 616, 131, 36, 40, 109, 580, 763, 22, 1010, 270

Offset: 1

Ivan Neretin, May 24 2015

nonn

Ivan Neretin, Table of n, a(n) for n = 1..1000

Cf. A258252.

A258254 Denominators of partial sums of 1/A258252(i), 1 <= i <= n.

Original entry on oeis.org

1, 2, 3, 1, 4, 3, 5, 2, 7, 5, 5, 6, 7, 1, 8, 6, 9, 3, 11, 8, 5, 12, 7, 9, 11, 2, 13, 11, 11, 14, 17, 3, 7, 4, 5, 11, 6, 13, 7, 8, 9, 10, 11, 12, 13, 1, 16, 12, 9, 15, 7, 20, 13, 19, 6, 17, 11, 16, 5, 14, 9, 13, 4, 11, 7, 17, 10, 13, 3, 23, 20, 17, 17, 12, 19, 7, 16, 9, 20

Offset: 1

Ivan Neretin, May 24 2015

nonn

Presumably, every natural number appears infinitely many times.

A258252(n) is a divisor of lcm(a(n-1), a(n)). The first case when it is a proper divisor (rather than that number itself) occurs at n=169.

Ivan Neretin, Table of n, a(n) for n = 1..25000

Cf. A258252, A002805 (analog for harmonic series).

A258255 Least k such that n <= Sum_{i=1..k} 1/A258252(i), where A258252 are the numbers having lowest possible denominators for the sums of reciprocals.

Original entry on oeis.org

1, 4, 14, 46, 153, 535, 1855, 6449, 22460, 81237

Offset: 1

Ivan Neretin, May 24 2015

Presumably, every natural number is reached at some step exactly, rather than "stepped over" (as is the case with harmonic series).

			For the first few terms of A258252, the sums of their reciprocal are: 1, 3/2, 5/3, 2, 9/4, 7/3, 12/5, 5/2, 18/7, 13/5, 14/5, 17/6, 20/7, 3, ... that are equal to 1, 2, 3 for n=1, 4, 14. So a(1)=1, a(2)=4, a(3)=14.

Cf. A258252, A004080 (analog for harmonic series), A002387.

cp's OEIS Frontend

A258253 Putative inverse of A258252.

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A258254 Denominators of partial sums of 1/A258252(i), 1 <= i <= n.

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A258255 Least k such that n <= Sum_{i=1..k} 1/A258252(i), where A258252 are the numbers having lowest possible denominators for the sums of reciprocals.

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