The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A295572 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A295572

First differences of A081881.
(history; published version)

#39 by Sean A. Irvine at Sat Jun 06 16:54:32 EDT 2020

STATUS

proposed

approved

#38 by G. C. Greubel at Sat Jun 06 14:26:15 EDT 2020

STATUS

editing

proposed

#37 by G. C. Greubel at Sat Jun 06 14:26:04 EDT 2020

FORMULA

a(1) = 1, a(n) = (max(m) : Sum_{s=r..m} 1/s <= 1)-r+1, r = Sum_{k=1..n-1} a(k). - Pablo Hueso Merino, Feb 16 2020

EXAMPLE

a(1) = 1 because 1 <= 1, 1 is one term (if you added 1/2 the sum would be greater than 1);.

a(2) = 2 because 1/2 + 1/3 = 0.8333... <= 1, 1/2 and 1/3 are two terms (if you added 1/4 the sum would be greater than one);.

MATHEMATICA

a[1] = 1;

a[n_] := a[n] = Module[{sum = 0}, r = 1 + Sum[a[k], {k, n - 1}];

p = x - 2;

p - r + 1];

CROSSREFS

Cf. A081881, A295571, A331030, A331028, A300897, A331028, A331030.

STATUS

proposed

editing

#36 by Michel Marcus at Mon May 04 04:59:30 EDT 2020

STATUS

editing

proposed

#35 by Michel Marcus at Mon May 04 04:59:25 EDT 2020

CROSSREFS

Cf. A081881, A295571, A331030, A331028, A300897.

STATUS

proposed

editing

#34 by Sean A. Irvine at Sun May 03 22:57:55 EDT 2020

STATUS

editing

proposed

#33 by Sean A. Irvine at Sun May 03 22:57:52 EDT 2020

COMMENTS

If the harmonic series is divided into the longest possible consecutive groups so that the sum of each group is <= 1, then a(n) is the number of terms in the n-th group. - Pablo Hueso Merino, Feb 16 2020

STATUS

proposed

editing

#32 by Vaclav Kotesovec at Sun Apr 05 04:21:18 EDT 2020

STATUS

editing

proposed

Discussion

Mon Apr 06

13:49

Wesley Ivan Hurt: I agree with Pablo.

#31 by Vaclav Kotesovec at Sun Apr 05 04:20:38 EDT 2020

FORMULA

a(n) ~ c * exp(n), where c = (exp(1)-1) * A300897 = 0.290142809280953235916025... - Vaclav Kotesovec, Apr 05 2020

STATUS

proposed

editing

#30 by Sean A. Irvine at Sat Mar 07 01:43:04 EST 2020

STATUS

editing

proposed

Discussion

Sat Mar 07

12:39

Pablo Hueso Merino: Sean, I think that it might be a good idea to explain that in each group there have to be the maximum amount of terms per group satisfying that their sum is <= 1, if we don't then there would be different possibilities to construct the sequence