The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A049765

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A049765

Triangular array T, read by rows: T(n,k) = (k mod n) + (n mod k), for k = 1..n and n >= 1.
(history; published version)

#20 by Charles R Greathouse IV at Thu Sep 08 08:44:58 EDT 2022

PROG

(MAGMAMagma) [[(k mod n) + (n mod k): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Dec 13 2019

Discussion

Thu Sep 08

08:44

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

#19 by Joerg Arndt at Sat Dec 14 08:14:26 EST 2019

STATUS

reviewed

approved

#18 by Michel Marcus at Sat Dec 14 02:59:08 EST 2019

STATUS

proposed

reviewed

#17 by G. C. Greubel at Fri Dec 13 16:49:31 EST 2019

STATUS

editing

proposed

#16 by G. C. Greubel at Fri Dec 13 16:49:24 EST 2019

LINKS

G. C. Greubel, <a href="/A049765/b049765.txt">Rows n = 1..100 of triangle, flattened</a>

MAPLE

seq(seq( `mod`(k, n) + `mod`(n, k), k = 1..n), n = 1..15); # G. C. Greubel, Dec 13 2019

MATHEMATICA

Table[Mod[k, n] + Mod[n, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Dec 13 2019 *)

PROG

(PARI) T(n, k) = k%n + n%k;

for(n=1, 15, for(k=1, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Dec 13 2019

(MAGMA) [[(k mod n) + (n mod k): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Dec 13 2019

(Sage) [[(k%n) + (n%k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Dec 13 2019

(GAP) Flat(List([1..15], n-> List([1..n], k-> (k mod n) + (n mod k) ))); # G. C. Greubel, Dec 13 2019

STATUS

approved

editing

#15 by Giovanni Resta at Thu Nov 21 07:44:12 EST 2019

STATUS

reviewed

approved

#14 by Joerg Arndt at Thu Nov 21 04:26:24 EST 2019

STATUS

proposed

reviewed

#13 by Michel Marcus at Thu Nov 21 02:31:21 EST 2019

STATUS

editing

proposed

Discussion

Thu Nov 21

02:33

Petros Hadjicostas: Sorry, I do not understand your question...

02:36

Michel Marcus: I simply added xref A048158

02:37

Michel Marcus: ok ?

02:41

Petros Hadjicostas: Yes, that is fine.

#12 by Michel Marcus at Thu Nov 21 02:30:40 EST 2019

CROSSREFS

Cf. A048158, A049767, A049768.

STATUS

proposed

editing

Discussion

Thu Nov 21

02:31

Michel Marcus: yes ... only this then ?

#11 by Petros Hadjicostas at Wed Nov 20 19:25:19 EST 2019

STATUS

editing

proposed

Discussion

Thu Nov 21

00:52

Michel Marcus: T(n, k) = A048158(n, k) +  Axxxx(n, k) but I did not find Axxx ??

01:14

Petros Hadjicostas: How about T(n,k) = A002262(n,k) + A048158(n, k) for 1 <= k <= n and n >= 1? (Or something like that?) Do you mind also checking?

01:25

Petros Hadjicostas: Actually, I am NOT right!  Each row of A002262 starts with 0 and then 1,2, .., n-1, while we need 1,2,...,n-1,0 in each row... (with 0 at end of each row for (n mod n)). So, I guess you are right: we cannot find (k mod n) for k = 1..n and rows n >= 1.

01:37

Petros Hadjicostas: I guess we can create  (k mod n) with rows indexed by n >= 1 and columns indexed by k (with 1 <= k <= n), but its *linear version* seq(seq(T(n,k), k=1..n), n=1..100) will be a shifted version of  A002262. I am not a fun of creating new sequences (especially, arrays) unless it is absolutely necessary.