The On-Line Encyclopedia of Integer Sequences (OEIS)

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The On-Line Encyclopedia of Integer Sequences (OEIS)

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Revision History for A367066

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

a(n) = ((Sum_{i=1..n} A367065(i))-2)/(n+2).
(history; published version)

#25 by Sean A. Irvine at Sat Dec 16 14:14:45 EST 2023

STATUS

proposed

approved

#24 by Zenan Sabanac at Thu Nov 09 02:05:13 EST 2023

STATUS

editing

proposed

Discussion

Thu Nov 09

02:23

Zenan Sabanac: All sections in line with the editor's comments and ready for approval.

#23 by Zenan Sabanac at Thu Nov 09 02:04:59 EST 2023

NAME

Avdispahić-Zejnulahi means sequence AZM(2): a(n) = ((Sum_{i=1..n} A367065(i))-2)/(n+2).

STATUS

proposed

editing

#22 by Andrew Howroyd at Sun Nov 05 14:22:43 EST 2023

STATUS

editing

proposed

Discussion

Sun Nov 05

14:32

Michel Marcus: I think the "Avdispahić-Zejnulahi means sequence AZM(2)" part of name should rather go to comments

14:32

Zenan Sabanac: Yes, that would be ok, thanks.

14:34

Zenan Sabanac: I would like to keep the title as proposed by Howroyd.

15:00

Jon E. Schoenfield: As I see it, it’s better to have the Name define the sequence in a way that’s as succinct as possible without making it hard to read, and to provide additional information in the Comments … so I agree with Michel….

For most OEIS readers who come across this sequence as a result of searching the OEIS looking for sequences that match a set of known terms, and who look to the Name field for a concise statement of the sequence’s basic mathematical definition, I doubt that the “Avdispahić-Zejnulahi means sequence AZM(2)” part will be helpful (although I would see it as useful information to include in the Comments).

But maybe several of the other editors see things differently … I don’t know. Perhaps more of them will weigh in on this.

Tue Nov 07

11:14

Zenan Sabanac: If possible, I would like to keep the name as propsed by Howroyd in honour of our late colleague Faruk Zejnulahi.

#21 by Andrew Howroyd at Sun Nov 05 14:22:24 EST 2023

NAME

Avdispahić-Zejnulahi means sequence AZM(2): a(n) = ((Sum_{i=1..n} A367065(i))-2)/(n+2).

STATUS

proposed

editing

Discussion

Sun Nov 05

14:22

Andrew Howroyd: Would this be ok as a compromise?

#20 by Andrew Howroyd at Sun Nov 05 14:18:21 EST 2023

STATUS

editing

proposed

#19 by Andrew Howroyd at Sun Nov 05 14:14:43 EST 2023

NAME

For a positive integer k and AZ(k) sequence {b(i)} (see A367065) define the Avdispahić-Zejnulahi means sequence AZM(k) by a(n) = ((Sum_{i=1..n} b(i))-k)/(n+k). This is the AZM(2) sequence. Thus, a(n)=((Sum_{i=1..n} A367065(i))-2)/(n+2).

a(n) = ((Sum_{i=1..n} A367065(i))-2)/(n+2).

COMMENTS

For a positive integer k define the Avdispahić-Zejnulahi sequence AZ(k) by b(1)=k, and thereafter b(n) is the least positive integer not yet in the sequence such that Sum_{i=1..n} b(i) == k (mod n+k). Define the Avdispahić-Zejnulahi means sequence AZM(k) by a(n) = ((Sum_{i=1..n} b(i))-k)/(n+k). This is the AZM(2) sequence.

CROSSREFS

A005379 without the starting term is the AZM(1) sequence.

Cf. A367065.

STATUS

proposed

editing

Discussion

Sun Nov 05

14:18

Andrew Howroyd: In this case, I think best to avoid the unwieldy name does not provide the definition of AZ(k). Moving this to the comments gives more space for a complete definition.

#18 by Zenan Sabanac at Sun Nov 05 13:46:17 EST 2023

STATUS

editing

proposed

#17 by Zenan Sabanac at Sun Nov 05 10:20:07 EST 2023

DATA

0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 32, 33, 34, 34, 35, 36, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 42, 43, 44, 44, 45, 45

LINKS

Muharem Avdispahić and Faruk Zejnulahi, <a href="https://www.researchgate.net/publication/341726940_AN_INTEGER_SEQUENCE_WITH_A_DIVISIBILITY_PROPERTY">An integer sequence with a divisibility property</a>, Fibonacci Quarterly, Vol. 58:4 (2020), 321-333.

PROG

with open('results.txt', 'w') as f:

f.write('M sequence:\n')

for i in range(1, 101):

f.write(strprint(m_list[i1:]))

if i != 100:

f.write(", ")

if i % 20 == 0:

f.write("\n")

CROSSREFS

The first 31 terms of AZM(2) match the consecutive 31 terms of A057361.

Additionally, the first 26 terms of the sequence correspond to the consecutive 26 terms of A136409, and the first 23 terms of the sequence align with the initial 23 terms of A123070.

Discussion

Sun Nov 05

10:29

Joerg Arndt: "Avdispahić-Zejnulahi means sequence AZM(k)" is that an established name?

10:43

Zenan Sabanac: For information regarding the name, please refer to Section 4 of J. Shallit's paper  <a href="https://arxiv.org/abs/2308.06544">Proving properties of some greedily-defined integer recurrences via automata theory</a>, arXiv:2308.06544 [cs.DM], 2023.

13:45

Zenan Sabanac: @Schoenfield It is work in progress in a paper we are preparing

#16 by Zenan Sabanac at Sun Nov 05 10:14:11 EST 2023

NAME

For a positive integer k and AZ(k) sequence {b(i)} (see A367065) define the Avdispahić-Zejnulahi means sequence AZM(k) by ma(n) = ((Sum_{i=1..n} b(i))-k)/(n+k). This is the AZM(2) sequence. Thus, a(n)=((Sum_{i=1..n} A367065(i))-2)/(n+2).