A028354 How the astronomical clock ("Orloj") in Prague strikes the hours (digits follow 12343212343... (A028356), n-th group adds to n).

1, 2, 3, 4, 32, 123, 43, 2123, 432, 1234, 32123, 43212, 34321, 23432, 123432, 1234321, 2343212, 3432123, 4321234, 32123432, 123432123, 43212343, 2123432123, 432123432, 1, 2, 3, 4, 32, 123, 43, 2123, 432, 1234, 32123, 43212

Offset: 1

Author

J. H. Conway

Keywords

• nonn
• nice
• base

Comments

There is a single bell, which to indicate 5 o'clock, say, strikes thrice then twice.

References

• Zdenek Horsky, "Prazsky Orloj" ["The Astronomical Clock of Prague", in Czech], Panorama, Prague, 1988, pp. 76-78.

Links

• Michal Krížek, Alena Šolcová and Lawrence Somer, Construction of Šindel sequences, Comment. Math. Univ. Carolin., 48 (2007), 373-388.
• N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

Crossrefs

Cf. A028355, A028356, A068962, A118382, A118383.

Programs

Mathematica

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] = If[k>24, a[k-24], Table[ s[i], {i, m[k]+1, n[k]}] // FromDigits]; Array[a, 36] (* Jean-François Alcover, Mar 13 2016 *)