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A053314
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a(n) contains n digits (either '1' or '4') and is divisible by 2^n.
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1
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4, 44, 144, 4144, 14144, 414144, 1414144, 41414144, 441414144, 1441414144, 11441414144, 411441414144, 4411441414144, 44411441414144, 444411441414144, 1444411441414144, 41444411441414144, 441444411441414144
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = a(n-1) + 10^(n-1)*(4 - 3*(a(n-1)/2^(n-1) mod 2)), i.e., a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 4, if not then n-th term begins with a 1.
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MAPLE
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A[1]:= 4:
for n from 2 to 100 do
if A[n-1] mod 2^n = 0 then A[n]:= A[n-1]+4*10^(n-1)
else A[n]:= A[n-1]+10^(n-1)
fi
od:
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MATHEMATICA
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nxt[{n_, a_}]:={n+1, If[Divisible[a, 2^(n+1)], 4*10^IntegerLength[a]+ a, 10^IntegerLength[ a]+a]}; NestList[nxt, {1, 4}, 20][[All, 2]] (* Harvey P. Dale, Oct 30 2022 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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