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A028355
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How the astronomical clock ("Orloj") in Prague would strike 1,2,3,...,24,25,.. (digits follow 12343212343... (A028356), n-th group adds to n).
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9
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1, 2, 3, 4, 32, 123, 43, 2123, 432, 1234, 32123, 43212, 34321, 23432, 123432, 1234321, 2343212, 3432123, 4321234, 32123432, 123432123, 43212343, 2123432123, 432123432, 1234321234, 32123432123, 43212343212
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OFFSET
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1,2
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COMMENTS
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This remarkable sequence is really a sequence of lists rather than numbers.
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REFERENCES
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Zdenek Horsky, "Prazsky Orloj" ["The Astronomical Clock of Prague", in Czech], Panorama, Prague, 1988, pp. 76-78.
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LINKS
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FORMULA
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a(n) = 1000001*a(n-15) - 1000000*a(n-30) for n > 30.
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)
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EXAMPLE
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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, ...
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MATHEMATICA
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s[i_] := {1, 2, 3, 4, 3, 2}[[Mod[i, 6, 1]]];
m[k_] := If[k == 1, 0, For[m0 = 1, True, m0++, If[k (k - 1)/2 == Sum[s[i], {i, 1, m0}], Return[m0]]]];
n[k_] := For[n0 = m[k] + 1, True, n0++, If[Sum[s[i], {i, m[k] + 1, n0}] == k, Return[n0]]];
a[k_] := a[k] = Table[s[i], {i, m[k] + 1, n[k]}] // FromDigits; Array[a, 27] (* Jean-François Alcover, Mar 14 2016 *)
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CROSSREFS
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KEYWORD
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nonn,nice,base
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AUTHOR
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STATUS
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approved
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