The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A231960

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A231960

Powers of 3 together with multiples of 6.
(history; published version)

#18 by Joerg Arndt at Fri Feb 28 13:07:07 EST 2014

STATUS

reviewed

approved

#17 by Ralf Stephan at Fri Feb 28 12:01:27 EST 2014

STATUS

proposed

reviewed

Discussion

Fri Feb 28

13:07

Joerg Arndt: Thomas Bridge owes you a beer or five...

#16 by Ralf Stephan at Fri Feb 28 12:01:03 EST 2014

STATUS

editing

proposed

#15 by Ralf Stephan at Fri Feb 28 11:59:23 EST 2014

COMMENTS

Also, 1 and 3*(even numbers m such that m divides A057083(m-1A005843) UNION powers of 3 (A008588)).

Also, numbers m such that m divides A057083(m-1), see the Smyth reference.

PROG

(Sage) def is_in_A231960(n):

return 6.divides(n) or n==3^valuation(n, 3)

CROSSREFS

Cf. A029744.

EXTENSIONS

Edited by Ralf Stephan, Feb 28 2014

Discussion

Fri Feb 28

12:01

Ralf Stephan: Boiled it down to essentials and added some.

#14 by Ralf Stephan at Fri Feb 28 11:39:07 EST 2014

NAME

Numbers n dividing the Lucas sequence u(n) = A057083(n-1).

Powers of 3 together with multiples of 6.

COMMENTS

All terms except 1 are divisible by 3. The sequence contains every nonnegative integer power of 3 and every (nonzero) multiple of 6.

Sequence is union Union of A000244 and A008588 (without 0).

Also, numbers m such that m divides A057083(m-1).

EXAMPLE

u(1,...,6)=1,3,6,9,9,0 and clearly n divides u(n) for n=1,3 and 6.

STATUS

proposed

editing

#13 by Joerg Arndt at Sun Feb 23 06:18:14 EST 2014

STATUS

editing

proposed

#12 by Joerg Arndt at Mon Jan 20 05:39:40 EST 2014

NAME

Numbers n dividing the Lucas sequence u(n) defined by u(i)=3*u(i-1)-3*u(i-2) with initial conditions u(0)=0, u(1)=1.

Numbers n dividing the Lucas sequence u(n) = A057083(n-1).

COMMENTS

Sequence is union of A000244 and A008588 (without 0).

EXAMPLE

u(0,1,...,6)=0,1,3,6,9,9,0 and clearly n divides u(n) for n=1,3 and 6.

CROSSREFS

Cf. Sequence is union of A000244 and A008588 (without 0).

Cf. A057083 is a subsequence (ignoring sign and excluding the term 0).

Discussion

Tue Feb 18

11:24

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A231960 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

Sun Feb 23

06:18

Joerg Arndt: Abandoned. Unless some editor wants to polish this one it should be recycled.

#11 by Thomas M. Bridge at Sat Dec 07 03:48:02 EST 2013

OFFSET

0,1,2

COMMENTS

All terms except 1 are divisible by 3. The sequence contains every nonnegative integer power of 3. There are infinitely many multiples and every (nonzero) multiple of 6 in the sequence.

CROSSREFS

Cf. Sequence is union of A000244 (powers of 3 and A008588 (subsequence)without 0).

Cf. A057083 is a subsequence (ignoring sign and excluding the term 0).

Discussion

Sat Dec 07

03:49

Thomas M. Bridge: The offset has been changed. It is the case that the sequence in fact contains every (nonzero) multiple of 6, which means a(n)-a(n-1)<7 is a clear consequence.

03:53

Thomas M. Bridge: I do not see how u(n) = A057083(n-1) for n>0. That sequence contains almost entirely odd numbers and this sequence contains almost entirely even numbers.

Sun Jan 19

18:05

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A231960 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#10 by Alois P. Heinz at Fri Dec 06 23:53:45 EST 2013

STATUS

proposed

editing

Discussion

Fri Dec 06

23:55

Alois P. Heinz: This is a list of numbers, the offset should be 1.

#9 by Thomas M. Bridge at Fri Dec 06 17:46:33 EST 2013

STATUS

editing

proposed

Discussion

Fri Dec 06

23:53

Alois P. Heinz: u(n) = A057083(n-1) for n>0.

Sat Dec 07

00:11

Farideh Firoozbakht: It seems that for each n, a(n)-a(n-1) < 7.