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A125144
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Increments in the number of decimal digits of 4^n.
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1
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1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0
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OFFSET
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1,1
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COMMENTS
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This sequence is not periodic because log(4)/log(10) is an irrational number. - T. D. Noe, Jan 25 2007
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LINKS
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FORMULA
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a(n)=Number_of_digits{4^(n+1)}-Number_of digits{4^(n)} with n>=0 and where "Number_of digits" is a hypothetical function giving the number of digits of the argument.
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EXAMPLE
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a(1)=1 because 4^(1+1)=16 (two digits) 4^1=4 (one digit) and the difference is 1.
a(2)=0 because 4^(2+1)=64 (two digits) 4^(2)=16 (two digits) and the difference is 0.
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MAPLE
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P:=proc(n) local i, j, k, w, old; k:=4; for i from 1 by 1 to n do j:=k^i; w:=0; while j>0 do w:=w+1; j:=trunc(j/10); od; if i>1 then print(w-old); old:=w; else old:=w; fi; od; end: P(1000);
# alternative:
H:= [seq(ilog10(4^i), i=1..1001)]:
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PROG
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(PARI) a(n) = #digits(4^(n+1)) - #digits(4^n); \\ Michel Marcus, Jul 12 2018
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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