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A097353
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Number of digits of the (10^n)-th tetranacci number (A000078(10^n)).
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1
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1, 2, 28, 284, 2849, 28500, 285008, 2850083, 28500834, 285008350, 2850083504, 28500835049, 285008350498, 2850083504986, 28500835049863, 285008350498633, 2850083504986335, 28500835049863359, 285008350498633597, 2850083504986335973
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OFFSET
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0,2
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COMMENTS
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a(n)/10^n converges to 0.28500835...
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LINKS
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FORMULA
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a(n) = floor(log_10(r) + (10^n-2)*log_10(x)) + 1 for n >= 1, where x is the positive real root of the tetranacci limit equation x^4 - x^3 - x^2 - x - 1 = 0, x = 1.92756... and r is the positive real root of the tetranacci auxiliary equation 563r^4 - 20r^2 - 5r - 1 = 0, r = 0.293813... - Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2007
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EXAMPLE
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Let t(n) = A000078(n). Then we have t(1) = 0, t(10) = 56, t(100) = 2505471397838180985096739296, with respectively 1, 2, 28 and 284 digits.
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MAPLE
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# This Maple code will at least get the first few terms correctly!
f:=proc(n) option remember; if n <= 2 then RETURN(0); fi; if n = 3 then RETURN(1); fi; f(n-1) + f(n-2) + f(n-3) +f(n-4); end; for n from 0 to 4 do lprint(f(10^n), length(f(10^n))); od;
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MATHEMATICA
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a = b = c = 0; d = i = 1; Do[e = a + b + c + d; a = b; b = c; c = d; d = e; If[n == 10^i, Print[Length[IntegerDigits[e]]]; i++ ], {n, 4, 10^6}] (* Ryan Propper, Jul 22 2005 *)
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PROG
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(PARI) \p 100 x=solve(x=1.9274, 1.9276, x^4-x^3-x^2-x-1); r=solve(x=0.2937, 0.2939, 563*x^4-20*x^2-5*x-1); for(k=1, 25, n=10^k; print1(floor( (log(r)+(n-2)*log(x))/log(10) )+1", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2007
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2007
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STATUS
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approved
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