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User talk:Ralf Stephan

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I get a HTTP 500 error when I go to the link you added:

Charles R Greathouse IV 20:48, 25 April 2013 (UTC)

This is odd because when I see the link in a browser which doesn't automatically log into Google I see my public profile, papers, and citations page. Can you try again? --Ralf Stephan 08:15, 27 April 2013 (UTC)


Hi. Thanks for the hint at the divisibility by 3. This made me calculate the prime factors, and they look quite interesting. There are a lot of prime factors of Fermat numbers (A023394). And there is the strange property, that the number of prime factors in the rows decreases (with few exceptions), although the numbers increase. If you discover any pattern in these numbers, please let me know. Greetings, Tilman Piesk 13:04, 3 August 2013 (UTC)

Yes, I noticed that. Ideally, we could find a formula in terms of other sequences, and I tried, but there was no quick hit. As you say, there might be hope to get at least some rules for the numbers in a row. - Ralf Stephan 06:36, 4 August 2013 (UTC)


Many thanks for your approval. This expansion originated from a question I posed twenty years ago during a meeting of math teachers: "How can we measure an angle with a compass only?". There is an article reporting the conclusions in the magazine published by our association, but it is in italian and so I suppose of no interest. I'm not expert in number theory and have very poor informations on ascending continued fractions, so I can't add any links to this subject. But it is possible that in OEIS there is someone that can do it. Greetings. Giovanni Artico 19:36, 13 September 2013 (UTC)


Am I right that what is wanted as a change to this program is removal of 1) ties to records, 2) end-primes for the records, and 3) the asterisks marking progress during waits (in the print commands)? In other words, am I not incorrect in asserting the program does what I want it to do and describe it as doing in square brackets before the program? An answer could save me a trip and a day in delay, if de-bugging or looking for a place my program as typed here has a bug need not be done.James G. Merickel 21:42, 6 October 2013 (UTC)

When I run your program I get
2:(2, 5) 3:(5, 13) 3:(19, 31) 3:(31, 43) 3:(61, 73) 3:(71, 83) 4:(83, 103) 4:(283, 313)
4:(443, 463) 4:(463, 491) 4:(617, 643) 4:(829, 859) 4:(859, 883) 4:(911, 941) 4:(1063, 1093)
4:(1433, 1453) 4:(1453, 1483) 5:(1627, 1669) 5:(1753, 1789)
I don't see how one gets the sequence from it:
2, 6, 8, 13, 16, 18, 19, 20, 21, 26, 28, 29, 31, 33, 34, 35, 36, 39, 40, 43, 45, 52
And it would be much better to change the program to output the sequence instead of adding lengthy comments about how to extract it. --Ralf Stephan 06:58, 7 October 2013 (UTC)

I think the change needed has been made, but I will return tonight if there is a real bug still. Otherwise, I have made a change to the print that perhaps was not really bothering you. It is done already, along with changes to comments. The bug was, I think, having a less-than where a greater-than was required in one place, but I will see. Re-submitted (but back later if wrong, as I said).James G. Merickel 21:25, 7 October 2013 (UTC)

I did have to return (switched the wrong inequality sign), but this should now be ready unless my original print is so much preferred to the changes made on that matter that I should just undo those.James G. Merickel 13:59, 8 October 2013 (UTC)

I still have preceding comments, but these are merely guides to how to obtain elements of the other sequences now (plus the meaning of the asterisks).James G. Merickel 12:52, 9 October 2013 (UTC)

Is there still a problem here (perhaps the asterisks or the way the sequence or its program are commented), or are you just not around to it yet? Sorry to bother if just a little delay.James G. Merickel 01:17, 10 October 2013 (UTC)

GCDs of sums of consecutive Fibonacci, Lucas numbers

You asked a question about A229339 in a pink box comment but Tony approved the draft before I could respond. Your question does deserve a response, so here goes.

Wed Oct 09 03:19

Ralf Stephan: Interesting. But there is a problem. How do you know that e.g. all 8-sums are divisible by 15? You cannot know unless you give a formula for 8-sums. I have held back similar sequences of my own where the numbers were conjectural.

I know that all sums of eight consecutive Lucas numbers are divisible by 15 by using arithmetic modulo 15. The Lucas numbers modulo 15 are 1, 3, 4, 7, 11, 3, 14, 2, 1, 3, 4, 7, 11, ... They have a period of 8. Then, 1 + 3 + 4 + 7 + 11 + 3 + 14 + 2 = 45 = 0 mod 15. So 15 is the minimum possible GCD. We see that 1 + 3 + 4 + 7 + 11 + 18 + 29 + 47 = 120 and 3 + 4 + 7 + 11 + 18 + 29 + 47 = 195. Then we verify that gcd(120,195) = 15, proving that 15 is indeed the GCD of all sums of eight consecutive Lucas numbers.
The Fibonacci numbers crop up in here naturally enough. Not satisfied with just modular arithmetic, I tried to figure out a formula 15x where x stands in for some polynomial. I'm not quite there yet, this is what I've got so far: \sum_{i = n}^{n + 7} L_i = 42L_{n + 1} + 33L_n = 75F_{n - 1} + 90F_n. (I don't have my notes in front of me at the moment, so I'm writing those from memory). Alonso del Arte 21:05, 9 October 2013 (UTC)
I agree that it's pretty safe to assume here that the modulo values are periodic, and thus the sequence values are good. It isn't always so however, and I hope you are aware of it. --Ralf Stephan 06:59, 10 October 2013 (UTC)
Can you give an example? I can't.
I was thinking about GCDs of all sums of n odd primes. Both you and I can prove that all sums of two consecutive odd primes are even. Both you and I can prove that some sums of three consecutive odd primes are coprime. Likewise for four and five consecutive odd primes. Maybe you can prove the general case, maybe you can't. But the values you and I present would not be conjectural. This does not depend on someone proving some long-standing conjecture nor on someone discovering a counterexample. Just because I lack the theoretic tools to prove the general case does not make my proof of individual cases "conjectural." Alonso del Arte 17:55, 11 October 2013 (UTC)
An example of a conjectural sequence not submitted is the draft A230044. I have already conceded that your case is not comparable. You may have misunderstood to what I referred when I wrote It isn't always so. --Ralf Stephan 06:04, 12 October 2013 (UTC)
Oh, I see, sorry. But... I don't know, I have this vague inkling that there's got to be a way at the very least to conclusively prove the small values of A230044... Alonso del Arte 02:49, 13 October 2013 (UTC)

Problem fixed

It appears there is a miscommunication. There was 1-character error in the transcription of the program referred to above. I have restored the program to its initial intent (but showing now each term on its own line). I have also brought A228851 in line with the massive editorial changes not specifically described or mentioned to me in the PUBLISHED A228850 that bears my name as author and REFERS TO the above. I'd appreciate it if you would also handle A228851 now.

As an aside, I've noticed that the sequence sign(A036263) has not been edited into the OEIS. This seems like a worthy addition. I'm not going to be at OEIS at all for the next 8 days. Massive project at residence.James G. Merickel 17:59, 13 October 2013 (UTC)STRIKE THIS! Because long strings of 0s and 1s show up first in search, to see A182394 and A079054 quickly requires many terms in search. I'm going to see if the two should be cross-referencing each other and are not before I leave.James G. Merickel 03:03, 14 October 2013 (UTC)I just edited into the previous the actual signum of A036263, as A079054 is its negative.James G. Merickel 03:24, 14 October 2013 (UTC)

I unfortunately had to make one more trip and edit (The prints originally had and should have the upper-case 'P' before the lower-case 'p').James G. Merickel 02:50, 14 October 2013 (UTC)

Tenured? Just guessing.James G. Merickel 16:45, 18 October 2013 (UTC)


I have written something about the sequences I've been adding and you can find it at It'll stay there 7 days, but let me know if you need me to post it again. It certainly does not have the formal rigour to be called a "paper". Let me know if you think it is useful and/or if you have suggestions on a more useful place to upload it. Thanks John Mason 22:09, 26 December 2013 (UTC)

This is fine as is (just add your name and date under the title) and you have several possibilities if you don't want to host it yourself: you can associate your file with the OEIS (we host it, see, or you use a general service like the very good WebCite ([1][2]). Or upload it to Google Drive, share it publicly, and put the link in your sequence entries; with a Google account you should additionally get access statistics of your shared files. --Ralf Stephan 07:11, 27 December 2013 (UTC)
Thanks John Mason 17:00, 28 December 2013 (UTC)
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