The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A122197 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A122197

Fractal sequence: count up to successive integers twice.
(history; published version)

#32 by Joerg Arndt at Tue Jun 25 01:31:00 EDT 2024

STATUS

reviewed

approved

#31 by Michel Marcus at Tue Jun 25 00:56:56 EDT 2024

STATUS

proposed

reviewed

#30 by Jon E. Schoenfield at Tue Jun 25 00:23:37 EDT 2024

STATUS

editing

proposed

#29 by Jon E. Schoenfield at Tue Jun 25 00:23:26 EDT 2024

COMMENTS

Fractal - deleting the first occurrence of each integer leaves the original sequence. Also, deleting the all the 1's leaves the original sequence plus 1. New values occur at square indices. 1's occur at indices m^2+1 and m^2+m+1. Ordinal transform of A122196.

Except for its initial 1, A122197 is the natural fractal sequence of A002620; that is, A122197(n+1) is the number of the row of A194061 that contains n. See A194029 for definition of natural fractal sequence. - Clark Kimberling, Aug 12 2011

FORMULA

a(n) = (A001477(n-1) mod A000194(n-1)) + 1 for n >= 2 with a(1) = 1.

a(n) = ((n - 1) mod (t+1)) + 1, where t = floor((sqrt(4*n-3)-1)/2). -

T(n, k) = A002260(n-k, k) . (End)

STATUS

approved

editing

#28 by Wesley Ivan Hurt at Sun Jan 09 00:19:47 EST 2022

STATUS

editing

approved

#27 by Wesley Ivan Hurt at Sun Jan 09 00:19:24 EST 2022

FORMULA

a(n) = A339399(2n-1). - Wesley Ivan Hurt, Jan 09 2022

CROSSREFS

Cf. A122196, A000290, A033638, A002260, A001477, A000194, A339399.

STATUS

approved

editing

#26 by Charles R Greathouse IV at Mon Jun 08 14:29:18 EDT 2020

STATUS

editing

approved

#25 by Charles R Greathouse IV at Mon Jun 08 14:29:03 EDT 2020

PROG

(PARI) a(n)=n - (sqrtint(4*n) + 1)\2*sqrtint(n-1) \\ Charles R Greathouse IV, Jun 08 2020

STATUS

proposed

editing

Discussion

Mon Jun 08

14:29

Charles R Greathouse IV: Neat formula!

#24 by Ridouane Oudra at Mon Jun 08 14:03:37 EDT 2020

STATUS

editing

proposed

#23 by Ridouane Oudra at Mon Jun 08 14:02:20 EDT 2020

FORMULA

a(n) = n - floor(sqrt(n) + 1/2)*floor(sqrt(n-1)). - Ridouane Oudra, Jun 08 2020

STATUS

approved

editing