The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A033819 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A033819

Trimorphic numbers: n^3 ends with n. Also m-morphic numbers for all m > 5 such that m-1 is not divisible by 10 and m == 3 (mod 4).
(history; published version)

#76 by Joerg Arndt at Fri Feb 09 10:09:25 EST 2024

STATUS

editing

approved

#75 by Paolo P. Lava at Fri Feb 09 09:13:16 EST 2024

MAPLE

P:=proc(n) if n^3 mod 10^(ilog10(n)+1)=n then n; fi; end:

seq(P(i), i=0..90625); # Paolo P. Lava, Jun 25 2018

STATUS

approved

editing

#74 by Alois P. Heinz at Wed Jan 17 15:03:00 EST 2024

STATUS

editing

approved

#73 by Alois P. Heinz at Wed Jan 17 15:02:35 EST 2024

COMMENTS

a(1) through a(13) are the rightmost digit or pair of digits in A215558. - Jonathan Vos Post, Aug 16 2012

CROSSREFS

Cf. A074194, A215558 (cubes of the terms).

STATUS

approved

editing

#72 by Charles R Greathouse IV at Thu Sep 08 08:44:51 EDT 2022

PROG

(MAGMAMagma) [n: n in [0..10^5] | Intseq(n^3)[1..#Intseq(n)] eq Intseq(n)]; // Bruno Berselli, Apr 04 2013

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#71 by Bruno Berselli at Mon May 20 02:48:48 EDT 2019

STATUS

reviewed

approved

#70 by Michel Marcus at Mon May 20 02:23:21 EDT 2019

STATUS

proposed

reviewed

#69 by Christopher Hohl at Sun May 19 22:54:08 EDT 2019

STATUS

editing

proposed

Discussion

Sun May 19

23:20

Jon E. Schoenfield: Thanks, Christopher!  Actually, a few days ago, I reached down to scritch one of my cats and somehow pulled a muscle in my back and am moving slowly :-(  ... but it's getting better.  :-)

23:25

Christopher Hohl: Sorry to hear that, but happy to hear you are on the mend!

Mon May 20

02:23

Michel Marcus: ok for me; I checked the formula for all terms in bfile

#68 by Christopher Hohl at Sun May 19 22:52:15 EDT 2019

COMMENTS

Let q(n) = floor(a(n)^3 / 10^A055642(a(n))), where A055642(n) is the number of digits in the decimal expansion of n. As well, let na and nb denote the indices of the preceding and next terms that begin with a 9. Then (1/q(n)) * (a(n)^4 - a(n)^3 - a(n)^2 + a(n)) - 2*a(n)^2 + a(n) + q(n) + 1 = a(na+nb-n)^2 - a(na+nb-n) - q(na+nb-n). - Christopher Hohl, Apr 08 2019

STATUS

proposed

editing

Discussion

Sun May 19

22:54

Christopher Hohl: Thanks Jon; hope you are well! Fixed.

#67 by Christopher Hohl at Sun May 19 21:16:32 EDT 2019

STATUS

editing

proposed

Discussion

Sun May 19

22:40

Jon E. Schoenfield: Need a space before the dash where you signed