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 Register FAQ Search Today's Posts Mark Forums Read 2005-09-13, 07:00 #1 Citrix   Jun 2003 32×52×7 Posts Sequence Generate a sequence where the N+1 term is the product of all previous terms +1 and the t(N+1) is divisible byp(N+1) ie the Nth prime. SO t(1) divisible by 1 t(2)=t(1)+1 and divisble by 2 t(3)=t(2)*t(1)+1 and divisble by 3 t(4)=t(3)*t(2)*t(1)+1 and divisble by 5. and so on... Good luck this is a hard problem, lets see who can generate the longest sequence. Can you find a algorithm to generate this sequence to some prime p? Citrix   2005-09-13, 07:24 #2 Citrix   Jun 2003 32×52×7 Posts There are multiple solution till each p but the smallest t(1) will be the correct one. Citrix   2005-09-14, 13:07 #3 Jushi   Sep 2005 UGent 22×3×5 Posts Let T = t(1). Then: t(2) = T + 1 t(3) = t(2)*t(1) + 1 = (T + 1)*T + 1 = T^2 + T + 1 t(4) = t(3)*t(2)*t(1) + 1 = (T^2 + T + 1)*(T + 1)*T + 1 = T^4 + 2T^3 + 2T^2 + T + 1 By looking modulo 5, the condition that t(4) is divisible by 5 is impossible. The best sequence is thus: t(1) = 1 t(2) = 2 t(3) = 3   2005-09-14, 23:00 #4 Citrix   Jun 2003 32×52×7 Posts cool solution, but the formula you generated for t4 is prime for 2,4,16,256. All 2^2^n. Pretty cool. Are there any other primes of the form 2^2^n? Citrix   2005-09-14, 23:23 #5 Citrix   Jun 2003 32·52·7 Posts Also prime for 2^(2^6)   2005-09-14, 23:33 #6 Citrix   Jun 2003 32×52×7 Posts no primes upto n=18  Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post kar_bon Aliquot Sequences 111 2020-11-27 20:13 sweety439 And now for something completely different 17 2017-06-13 03:49 devarajkandadai Math 1 2007-08-25 15:23 devarajkandadai Math 3 2007-03-20 19:43 biwema Puzzles 13 2004-06-11 02:05

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