The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A033951

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A033951

Write 1,2,... in a clockwise spiral; sequence gives numbers on positive x axis.
(history; published version)

#69 by Jarrod G. Sage at Wed Jul 17 15:52:10 EDT 2024

COMMENTS

a(n) is "n" less than the n-th odd square. - Jarrod G. Sage, Jul 16 2024

#68 by Jarrod G. Sage at Wed Jul 17 15:50:42 EDT 2024

COMMENTS

Indexed from zero, a(n) is "n" less than the n-th odd square. - Jarrod G. Sage, Jul 16 2024

#67 by Joerg Arndt at Wed Jul 17 11:08:59 EDT 2024

STATUS

proposed

Discussion

Wed Jul 17

12:46

Andrew Howroyd: First comment is just Reinhard Zumkeller, May 17 2009 formula in words.

#66 by Jarrod G. Sage at Tue Jul 16 22:26:29 EDT 2024

STATUS

editing

Discussion

Wed Jul 17

02:49

Michel Marcus: 1st comment: rather write a formula

05:04

Michel Marcus: Indexed from zero ?  offset is 0, so already indexed from 0

#65 by Jarrod G. Sage at Tue Jul 16 22:21:15 EDT 2024

COMMENTS

STATUS

approved

Discussion

Tue Jul 16

22:26

Jarrod G. Sage: I added that indexed from zero the sequence is the n less than the n-th odd square—this can be see from attaching the spiral to a grid and taking the minimal square centered at 1 that includes a(n). That square has dimensions 2n+1 by 2n+1, and a(n) is definitionally at the position n+1 position of its column, so there are "n" values greater than a(n) in the square and a(n) = (2n+1)^2-n. This same logic can be used to identify the value of the 2x1 diagonal in A081344.

#64 by Alois P. Heinz at Wed Apr 24 19:49:03 EDT 2024

STATUS

proposed

#63 by Stefano Spezia at Wed Apr 24 15:00:53 EDT 2024

STATUS

editing

#62 by Stefano Spezia at Wed Apr 24 14:39:09 EDT 2024

DATA

1, 8, 23, 46, 77, 116, 163, 218, 281, 352, 431, 518, 613, 716, 827, 946, 1073, 1208, 1351, 1502, 1661, 1828, 2003, 2186, 2377, 2576, 2783, 2998, 3221, 3452, 3691, 3938, 4193, 4456, 4727, 5006, 5293, 5588, 5891, 6202, 6521, 6848, 7183, 7526, 7877, 8236

#61 by Stefano Spezia at Wed Apr 24 13:02:03 EDT 2024

CROSSREFS

Cf. A132774.

#60 by Stefano Spezia at Wed Apr 24 13:00:29 EDT 2024

FORMULA

STATUS

approved