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A371032
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a(n) is the integer whose decimal digits are 0's or 1's in alternating runs of lengths n, n-1, n-2, ..., 3, 2, 1.
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3
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1, 110, 111001, 1111000110, 111110000111001, 111111000001111000110, 1111111000000111110000111001, 111111110000000111111000001111000110, 111111111000000001111111000000111110000111001, 1111111111000000000111111110000000111111000001111000110
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (10^(n*(n+1)/2) - 1)/9 - a(n-1). - Robert Israel, Jul 09 2024
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EXAMPLE
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a(1) = 1 has runlength 1; a(2) = 110 has runlengths 2,1; a(3) = 111001 has runlengths 3,2,1.
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MAPLE
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f:= proc(n) option remember; (10^(n*(n+1)/2)-1)/9 - procname(n-1) end proc:
f(1):= 1:
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MATHEMATICA
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Flatten[Table[Flatten[Map[ConstantArray[Mod[#, 2], n + 1 - #] &, Range[n]]], {n, 10}]] (* Peter J. C. Moses, Mar 08 2024 *)
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PROG
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(Python)
c = 0
for i in range(n):
c = (m:=10**(n-i))*c
if i&1^1:
c += (m-1)//9
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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