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Revision History for A356063 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

a(n) is the new Lucas divisor that appears at the step A356062(n).
(history; published version)

#11 by Michael De Vlieger at Wed Aug 31 13:32:04 EDT 2022

STATUS

reviewed

approved

#10 by Michel Marcus at Wed Aug 31 06:37:35 EDT 2022

STATUS

proposed

reviewed

Discussion

Wed Aug 31

07:20

Jon E. Schoenfield: I think the Name here isn’t quite right…

07:23

Jon E. Schoenfield: At n=6, the Name becomes “a(6) is the new Lucas divisor that appears at the step A356062(6).” So “7 is the new Lucas divisor that appears at the step 252.” (“at the step 252” seems bad.)

10:07

Bernard Schott: Ah, yes: “a(6) is the new Lucas divisor that appears at the step A356062(6)".

10:08

Bernard Schott: Now, A356062(6) = 252 and the set of the six Lucas divisors of 252 is {1, 2, 3, 4, 7, 18}. Also A356062(5) = 36 and the set of the five Lucas divisors of 36 is {1, 2, 3, 4, 18}.

10:10

Bernard Schott: Hence, the new Lucas divisor that appears at the step A356062(6) = 252 is {1, 2, 3, 4, 7, 18} \ {1, 2, 3, 4, 18} = {7}; hence, a(6) = 7. Please, see also in example section, how is calculated a(7).

10:10

Bernard Schott: Conclusion: I think the Name here is quite right and perfect…

13:32

Michael De Vlieger: We can adjust after approval; Michel reviewed.

#9 by Bernard Schott at Wed Jul 27 11:30:01 EDT 2022

STATUS

editing

proposed

Discussion

Wed Jul 27

11:50

Bernard Schott: Proposed conjecture.

Fri Jul 29

03:08

David A. Corneth: If this sequence is well defined it should be fairly easy to find terms. We could give it armbands by looking at new Lucas divisors of LCM(A356062(1),...,A356062(n)).

03:08

David A. Corneth: If that's needed computation becomes quite a bit tougher I think

#8 by Bernard Schott at Wed Jul 27 11:29:28 EDT 2022

COMMENTS

Conjecture: the sequence is well defined, i.e., it is not possible that two new Lucas divisors arrive while one disappears for some step in A356062.

STATUS

proposed

editing

#7 by Bernard Schott at Wed Jul 27 09:20:38 EDT 2022

STATUS

editing

proposed

#6 by Bernard Schott at Wed Jul 27 09:14:43 EDT 2022

DATA

1, 2, 4, 3, 18, 7, 11, 76, 322, 29, 1364, 123, 47, 199, 24476, 843, 5778, 521

Discussion

Wed Jul 27

09:16

Bernard Schott: Up to A356062(18) = 4140956578896459860267268 where Lucas divisor 521 appears, this sequence is well defined.

#5 by Bernard Schott at Wed Jul 27 08:55:48 EDT 2022

DATA

1, 2, 4, 3, 18, 7, 11, 76, 322, 29, 123, 47, 199, 24476

#4 by Bernard Schott at Wed Jul 27 08:13:55 EDT 2022

DATA

1, 2, 4, 3, 18, 7, 11, 76, 322, 29, 123, 47

STATUS

proposed

editing

#3 by Bernard Schott at Mon Jul 25 11:50:59 EDT 2022

STATUS

editing

proposed

Discussion

Tue Jul 26

08:54

Michel Marcus: not really convinced by this sequence

09:31

Michel Marcus: what if 2 new Lucas divisors arrive and 1 disappears ?

09:36

Michel Marcus: for instance it happens for the next instance of A356062 : 5, 3, 6, 18, 72, 396, 4788 (with 2nd least instead of least)

Wed Jul 27

00:56

Bernard Schott: 09:31 Up to now, this is not the case, but I cannot prove that does not arrive later, even if it could be rather exceptional.

01:15

Bernard Schott: 09:36 Très joli; Lucas divisors of 396 are {1, 2, 3, 4, 11, 18}and Lucas divisors of 4788 are {1, 2, 3, 4, 7, 18, 76}, so 11 disappears and 7 and 76 appear. Nice counter-example, even if it is not the least but the second least.

01:17

Bernard Schott: 08:54 If you are "not really convinced by this sequence", (up to now, this sequence is well defined), go to recycle.

03:26

Michel Marcus: I kind of think the same for A349100

03:32

Bernard Schott: Yes Michel, I know, it is near the same: A349100 is for records with Fibonacci divisors while here it is for smallest integers with n Lucas divisors.

03:37

Bernard Schott: In both cases, for known terms, the sequence of smallest integers with n (Lucas or Fibonacci) divisors coincide with the sequence of integers that set a new record for number of (Lucas or Fibonacci) divisors.

#2 by Bernard Schott at Mon Jul 25 11:49:58 EDT 2022

NAME

allocated for Bernard Schotta(n) is the new Lucas divisor that appears at the step A356062(n).

DATA

1, 2, 4, 3, 18, 7, 11, 76, 322, 29

OFFSET

1,2

COMMENTS

The sequence is not monotonic.

EXAMPLE

a(1) = 1 because the smallest integer that has only one Lucas divisor is 1 since 1 is the smallest Lucas number in A000032.

A356062(6) = 252 and the set of the six Lucas divisors of 252 is {1, 2, 3, 4, 7, 18}. Then, A356062(7) = 2772 and the set of the seven Lucas divisors of 2772 is {1, 2, 3, 4, 7, 11, 18}. The new Lucas divisor that appears in this set is 11, hence a(7) = 11.

CROSSREFS

Cf. A000032, A304092, A349100, A356062.

KEYWORD

allocated

nonn,more

AUTHOR

Bernard Schott, Jul 25 2022

STATUS

approved

editing