The On-Line Encyclopedia of Integer Sequences (OEIS)

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Revision History for A343586 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

a(n) = the sum of all the multiples of 2 or 5 less than or equal to 10^n.
(history; published version)

#35 by N. J. A. Sloane at Sat Sep 18 00:39:38 EDT 2021

STATUS

editing

approved

#34 by N. J. A. Sloane at Sat Sep 18 00:39:18 EDT 2021

LINKS

Nicolo Sartori di Borgoricco, <a href="https:/A343586/www.overleafa343586.com/read/rnxtyxzbnvhrpdf">Proof of sequence occurrencethat formula is correct</a>.

Nicolo Sartori di Borgoricco, <a href="/A343586/a343586.pdf">Sequence proof</a>

STATUS

approved

editing

Discussion

Sat Sep 18

00:39

N. J. A. Sloane: Deleted duplicate link

#33 by N. J. A. Sloane at Sat Sep 18 00:32:14 EDT 2021

NAME

a(n) is = the sum of all the multiples of 2 or 5 less than or equal to 10^n.

COMMENTS

It can be proven that, upon doing the same summing process, a similar pattern appears only when using multiples of 2, 3 or 5 (in any combination); it is particularly neat when using 2 and 5 as they are factors of 10. - Nicolo Sartori di Borgoricco, Aug 10 2021

CROSSREFS

Cf. A065502 (multiples of 2 or 5), A281787 (sum of multiples of 3 or 5).

STATUS

proposed

approved

#32 by Michel Marcus at Wed Aug 11 02:40:49 EDT 2021

STATUS

editing

proposed

Discussion

Wed Aug 11

02:45

Joerg Arndt: I don't get what the comment is supposed to say.

12:28

Nicolo Sartori di Borgoricco: I mean that if you sum all of the multiples of 3 or 5, or, 2 or 5, or, 2 or 3, or, 2 or 3 or 5 up to and including a power of 10, you will get a similar pattern in  the sequence where each term is the sum obtained when the upper bound is changed to the next power of ten up (a1 = sum up to 10, a2 = sum up to 100,  a3 = sum up to 1000 etc). As in that the digits of the terms never change, the next term just physically looks like it's a "stretched out" version of the previous term. These "stretching terms" only appear when the summing process is done with the following primes: 2 or 3 or 5, in some combination

Sat Aug 14

08:47

Kevin Ryde: At "similar pattern" it's not really clear what that means, if you can put something brief.  Can refer to A281787 on what it's pattern looks like.  I don't find a sequence for 2 and 3 which would be the other combination.  Bigger divisors still have a repeating pattern of digits, but longer than 1 yes?  (Maybe always?, or at least "in general".)

Thu Aug 19

06:38

Nicolo Sartori di Borgoricco: Yes, generally with larger divisors you get terms with varying digits and not much of pattern (compared to this sequence whose terms only contain 3, 0, or 5). The sequence for 2 and 3 also works it just hasn’t been published to the OEIS. By similar I mean that the terms look like this: ABBBCBBBA, ABBBBCBBBBA, etc (or sometimes the middle will contain BCCB or BCDB)

Tue Aug 24

16:36

Sean A. Irvine: For me, this comment is too vague for inclusion.

Sat Sep 18

00:32

N. J. A. Sloane: I agree with Sean

#31 by Michel Marcus at Wed Aug 11 02:40:45 EDT 2021

NAME

a(n) = is the sum of all the multiples of 2 or 5 less than or equal to 10^n.

STATUS

proposed

editing

#30 by Amiram Eldar at Tue Aug 10 12:04:16 EDT 2021

STATUS

editing

proposed

#29 by Amiram Eldar at Tue Aug 10 12:04:13 EDT 2021

COMMENTS

It can be proven that, upon doing the same summing process, a similar pattern appears only when using multiples of 2, 3 or 5 (in any combination); it is particularly neat when using 2 and 5 as they are factors of 10. _- _Nicolo Sartori di Borgoricco_, Aug 10 2021

STATUS

proposed

editing

#28 by Nicolo Sartori di Borgoricco at Tue Aug 10 12:02:04 EDT 2021

STATUS

editing

proposed

#27 by Nicolo Sartori di Borgoricco at Tue Aug 10 12:01:44 EDT 2021

COMMENTS

It can be proven that, upon doing the same summing process, a similar pattern appears only when using multiples of 2, 3 or 5 (in any combination); it is particularly neat when using 2 and 5 as they are factors of 10._ _Nicolo Sartori di Borgoricco_, Aug 10 2021

#26 by Nicolo Sartori di Borgoricco at Tue Aug 10 12:00:36 EDT 2021

COMMENTS

It can be proven that, upon doing the same summing process, a similar pattern appears only when using multiples of 2, 3 or 5 (in any combination); it is particularly neat when using 2 and 5 as they are factors of 10. __Nicolo Sartori di Borgoricco_, Aug 08 10 2021