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 A118383 Unrefined Orloj clock sequences; row n sums to n. 4
 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 4, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 2, 2, 3, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 4, 2, 1, 2, 3, 3, 1, 2, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS An Orloj clock sequence is a finite sequence of positive integers that, when iterated, can be grouped so that the groups sum to successive natural numbers. There is one unrefined sequence whose values sum to each n; all other Orloj clock sequences summing to n can be obtained by refining this one. Refining means splitting one or more terms into values summing to that term. (The unrefined sequence for n = 2^k*(2m-1) is the sequence for 2m-1 repeated 2^k times, but any single refinement - possible unless m = 1 - will produce an aperiodic sequence summing to n.) The Orloj clock sequence is the one summing to 15: 1,2,3,4,3,2, with a beautiful up and down pattern. LINKS Wikipedia, Prague astronomical clock FORMULA Let b(i),0<=i n, tri -= n); found[tri] = 1); last = 0; r = []; for(i = 1, n, if(found[i], r = concat(r, [i-last]); last = i)); r} for (n=1, 10, print(Orloj(n))) CROSSREFS Cf. A028355, A118382. Length of row n is A117484(n). Sequence in context: A329037 A279794 A025900 * A115766 A108339 A138559 Adjacent sequences:  A118380 A118381 A118382 * A118384 A118385 A118386 KEYWORD nonn,tabf AUTHOR Franklin T. Adams-Watters, Apr 26 2006 STATUS approved

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Last modified June 5 09:58 EDT 2020. Contains 334840 sequences. (Running on oeis4.)