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A282622
Number of digits of the representation of n in the alternating sexagesimal-decimal number system.
3
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
OFFSET
1,10
COMMENTS
For a(1)..a(59) this sequence coincides with A055642.
For the alternating sexagesimal-decimal number system see a comment in A055643.
FORMULA
a(n) = 1 for n = 1..9, a(n) = 2 for n = 10..59, a(n) = 3 for n = 60..599, a(n) = 4 for n = 600..3600, ..., i.e., a(n) = k, k >= 1, for n = A281863(k-1)..A281863(k)-1.
MATHEMATICA
With[{nn = 120}, IntegerLength[Range@ 120, MixedRadix[Flatten@ ConstantArray[{6, 10}, {2 Ceiling@ Log[60, nn]}]]]] (* Version 10.2, or *)
Table[StringLength@ If[StringTake[#, 1] == "0", StringDrop[#, 1], #] &@ StringJoin@ Map[If[# < 10, StringJoin["0", ToString@ #], ToString@ #] &, IntegerDigits[n, 60]], {n, 120}] (* Michael De Vlieger, Feb 20 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 20 2017
STATUS
approved