Timeline for Does a sequence of primes defined like this exists?
Current License: CC BY-SA 3.0
22 events
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| Mar 31, 2018 at 12:41 | comment | added | Shalom | @მამუკაჯიბლაძე I think that all your computational data and all that you succeeded to observe would fit in a nice answer, if you want to post it. | |
| Mar 24, 2018 at 9:38 | history | edited | Shalom | CC BY-SA 3.0 |
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| Mar 24, 2018 at 7:12 | answer | added | Aaron Meyerowitz | timeline score: 2 | |
| Mar 23, 2018 at 19:45 | comment | added | მამუკა ჯიბლაძე | It generates the greedy sequence of length n starting with the mth prime (if it has prime ds to begin with) | |
| Mar 23, 2018 at 19:44 | comment | added | მამუკა ჯიბლაძე |
Here is Mathematica code in case you would like to use it genseq[n_, m_] := genseq[n, m] = If[n == 1, If[Not[PrimeQ[Total[IntegerDigits[Prime[m]]]]], {}, {Prime[m]}], Module[{s = genseq[n - 1, m], pr, k}, pr = Times @@ s; If[Not[PrimeQ[Total[IntegerDigits[pr]]]], Return[{}]]; k = PrimePi[Last[s]] + 1; While[Not[PrimeQ[Total[IntegerDigits[pr Prime[k]]]]], k++]; Append[s, Prime[k]] ] ]
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| Mar 23, 2018 at 19:44 | comment | added | მამუკა ჯიბლაძე | This sounds even more obscure, sorry | |
| Mar 23, 2018 at 19:43 | comment | added | Shalom | @მამუკაჯიბლაძე Did you try to start with some prime, for example 2, and then choose as next primes only primes of the form 6k+1 or only primes of the form 6k+5 and then observed the jumps? | |
| Mar 23, 2018 at 19:40 | comment | added | მამუკა ჯიბლაძე | Frankly speaking I agree with @GeraldEdgar - you should provide some motivation in the question, otherwise it looks too obscure to stimulate any reaction | |
| Mar 23, 2018 at 19:39 | comment | added | Shalom | @მამუკაჯიბლაძე I have some ideas. | |
| Mar 23, 2018 at 19:34 | comment | added | მამუკა ჯიბლაძე | Well I don't think I can produce anything interesting beyond what I already did | |
| Mar 23, 2018 at 19:27 | comment | added | Shalom | @მამუკაჯიბლაძე It cannot be for 3 because it would produce digit sums that are only multiples of 3. Should we make a chat room for this and some other problems? | |
| Mar 23, 2018 at 19:26 | comment | added | მამუკა ჯიბლაძე | There seems to be no such sequence starting with 3. With all other starting primes I checked so far it seems to be as dense as for 2 | |
| Mar 23, 2018 at 19:13 | comment | added | Shalom | @მამუკაჯიბლაძე That also comes as a surprise. Did you check some other primes other than 2 as starting points and observed the jumps? | |
| Mar 23, 2018 at 19:12 | comment | added | მამუკა ჯიბლაძე | jumps in the sequence are over 3, 2, 3, 2, 7, 1, 5, 1, 5, 6, 4, 4, 1, 7, 7, 6, 1, 7, 2, 3, 1, 1, 6, 3, 1, 1, 5, 2, 6, 16, 5, 5, 15, 2, 2, 1, 2, 1, 3, 8, 1, 6, 3, 1, 1, 5, 1, 2, 3, 6, 11, 3, 5, 4, 10, 3, 5, 3, 6, 4, 2, 1, 4, 2, 1, 4, 3, 4, 1, 1, 14, 14, 5, 6, 13, 3, 3, 15, 6, 1, 6, 2, 6, 16, 4, 5, 3, 12, 1, 10, 4, 4, 4, 16, 2, 6, 3, 11, 4, 6, 1, 9, 7, 10, 1, 4, 11, 3, 1, 3, 2, 5, 3, 2, 2, 4, 4, 12, 7, 1, 10, 10, 8, 3, 3, 2, 20, 3, 10, 3, 6, 1, 1, 5, 3, 15, 6, 1, 14, 4, 3, 9, 5, 1, 7, 1, 6, 1, 1, 1, 4, 2, 15, 7, 3, 14, 4, 2, 4, 3, 9, 6, 2, ... consecutive primes - they do not seem to grow much | |
| Mar 23, 2018 at 19:09 | comment | added | Shalom | @მამუკაჯიბლაძე Your sequence is "denser" than I would ever expect. It also contains some twin primes. | |
| Mar 23, 2018 at 19:06 | comment | added | მამუკა ჯიბლაძე | The "greedy" strategy does not seem to get stuck easily - so far I've reached 1000; the sequence starts with 2, 7, 13, 23, 31, 61, 67, 89, 97, 113, 151, 173, 193, 197, 239, 277, 313, 317, 367, 379, 397, 401, 409, 443, 461, 463, 467, 503, 521, 569, 659, 691, 733, 829, 853, 859, 863, 881, 883, 911, 971, 977, 1019, 1033, 1039, 1049, 1087, 1091, 1097, 1117, 1171, 1249, 1279, 1301, 1321, 1429, 1447, 1481, 1489, 1543, 1567, 1579, 1583, 1609, 1619, 1621, 1663, 1693, 1721, 1723, 1733, 1861, 1973, 1999, 2039, 2137, 2153, 2203, 2309, 2351, 2357, 2393, 2411, 2459, 2617, 2657, 2683, 2693, 2777, 2789, ... | |
| Mar 23, 2018 at 18:55 | history | edited | Shalom | CC BY-SA 3.0 |
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| Mar 23, 2018 at 18:55 | comment | added | Shalom | @მამუკაჯიბლაძე Yes. | |
| Mar 23, 2018 at 18:50 | comment | added | მამუკა ჯიბლაძე | Do you mean a strictly increasing sequence of primes or? | |
| Mar 23, 2018 at 17:48 | comment | added | Shalom | @GeraldEdgar Yes, base 10. It does not need to be "of use". But there is no reason why it shouldn´t be developed, first as a part of pure mathematics, more specially ,number theory, and an "uses" come later, if there would be any. | |
| Mar 23, 2018 at 17:38 | comment | added | Gerald Edgar | Is that base ten digit sum? If so, it seems to me it is a rather unnatural thing to consider. Indeed, I expect there are no books on "digit-sum theory" because it has (so far) been use for very little. | |
| Mar 23, 2018 at 17:24 | history | asked | Shalom | CC BY-SA 3.0 |