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%I #33 Apr 19 2024 01:59:24
%S 1,2,3,4,32,123,43,2123,432,1234,32123,43212,34321,23432,123432,
%T 1234321,2343212,3432123,4321234,32123432,123432123,43212343,
%U 2123432123,432123432,1234321234,32123432123,43212343212
%N How the astronomical clock ("Orloj") in Prague would strike 1,2,3,...,24,25,.. (digits follow 12343212343... (A028356), n-th group adds to n).
%C This remarkable sequence is really a sequence of lists rather than numbers.
%D Zdenek Horsky, "Prazsky Orloj" ["The Astronomical Clock of Prague", in Czech], Panorama, Prague, 1988, pp. 76-78.
%H Seiichi Manyama, <a href="/A028355/b028355.txt">Table of n, a(n) for n = 1..2500</a>
%H Michal Krížek, Alena Šolcová and Lawrence Somer, <a href="http://dml.cz/dmlcz/119666">Construction of Šindel sequences</a>, Comment. Math. Univ. Carolin., 48 (2007), 373-388.
%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/sg.txt">My favorite integer sequences</a>, in Sequences and their Applications (Proceedings of SETA '98).
%F Conjectures from _Chai Wah Wu_, Apr 18 2024: (Start)
%F a(n) = 1000001*a(n-15) - 1000000*a(n-30) for n > 30.
%F G.f.: x*(100000*x^28 + 200000*x^27 + 300000*x^26 + 400000*x^25 + 320000*x^24 + 123000*x^23 + 430000*x^22 + 212300*x^21 + 432000*x^20 + 123400*x^19 + 321230*x^18 + 432120*x^17 + 343210*x^16 + 234320*x^15 + 123432*x^14 + 23432*x^13 + 34321*x^12 + 43212*x^11 + 32123*x^10 + 1234*x^9 + 432*x^8 + 2123*x^7 + 43*x^6 + 123*x^5 + 32*x^4 + 4*x^3 + 3*x^2 + 2*x + 1)/(1000000*x^30 - 1000001*x^15 + 1). (End)
%e 1, 2, 3, 4, 3+2=5, 1+2+3=6, 4+3=7, 2+1+2+3=8, 4+3+2=9, 1+2+3+4=10, 3+2+1+2+3=11, 4+3+2+1+2=12, 3+4+3+2+1=13, 2+3+4+3+2=14, 1+2+3+4+3+2=15, ...
%t s[i_] := {1, 2, 3, 4, 3, 2}[[Mod[i, 6, 1]]];
%t m[k_] := If[k == 1, 0, For[m0 = 1, True, m0++, If[k (k - 1)/2 == Sum[s[i], {i, 1, m0}], Return[m0]]]];
%t n[k_] := For[n0 = m[k] + 1, True, n0++, If[Sum[s[i], {i, m[k] + 1, n0}] == k, Return[n0]]];
%t a[k_] := a[k] = Table[s[i], {i, m[k] + 1, n[k]}] // FromDigits; Array[a, 27] (* _Jean-François Alcover_, Mar 14 2016 *)
%Y Cf. A028354, A028356, A068962, A118382, A118383.
%K nonn,nice,base,changed
%O 1,2
%A _N. J. A. Sloane_, _J. H. Conway_
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