# A Question to Trouble Even the Best of You

Tags: trouble
 P: 15,294 What is an "arithmetical sequence"?
 P: 998 An arithmetic sequence is one of the form $(n,n+k,n+2k,n+3k,...,n+mk,...)$.
P: 363
 Quote by Data About five seconds . It makes sense to start at 7; if you can find a sequence starting with 7 that has spacing smaller than 210 (and there's no smaller sequence starting with 7), then that's obviously the smallest one.
Ah,yes,yes,...
To me it makes sense to start with 199 and find "minimum" prime-sequence of 10 terms with spacing 210 :

$$199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089$$.

But it took me longer time ,about 10 seconds
P: 681
 Quote by DaveC426913 What is an "arithmetical sequence"?
I've written a mini-introduction to arithmetic progressions here
 P: 27 what about 31,41,51,61,71,81,91 ? are there any non-primes in there? but even if that is right (i doubt it is, i'm too tired to see the factors i probably should) i cheated b/c i guessed
P: 1,076
 Quote by mr200backstrok what about 31,41,51,61,71,81,91 ? are there any non-primes in there? but even if that is right (i doubt it is, i'm too tired to see the factors i probably should) i cheated b/c i guessed
51 and 81 are both composite.
 P: 27 oh haha 9*9 = 81 yep im tired Any idea where i could get a description of the concepts they are talking about? (I don't want to hijack the thread)
P: 998
 Quote by mr200backstrok Any idea where i could get a description of the concepts they are talking about? (I don't want to hijack the thread)
All I used for this problem was a little bit of modular arithmetic.

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