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A120437
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Differences of A037314 (sum of base-3 digits of n = sum of base-9 digits of n).
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2
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1, 1, 7, 1, 1, 7, 1, 1, 61, 1, 1, 7, 1, 1, 7, 1, 1, 61, 1, 1, 7, 1, 1, 7, 1, 1, 547, 1, 1, 7, 1, 1, 7, 1, 1, 61, 1, 1, 7, 1, 1, 7, 1, 1, 61, 1, 1, 7, 1, 1, 7, 1, 1, 547, 1, 1, 7, 1, 1, 7, 1, 1, 61, 1, 1, 7, 1, 1, 7, 1, 1, 61, 1, 1, 7, 1, 1, 7, 1, 1
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OFFSET
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1,3
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COMMENTS
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It appears that sign(a(n+1) - a(n)) gives A102283. - Filip Zaludek, Oct 29 2016
This is clear: a(n) = 1 for n == 1 or 2 (mod 3), and a(n) >= 7 for n == 0 (mod 3): see comment by Franklin T. Adams-Watters on A037314. - Robert Israel, Nov 06 2016
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LINKS
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Michel Marcus, Table of n, a(n) for n = 1..2000
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FORMULA
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It appears that the sequence is given by the following recursion: a(n)=1 if n=1, a(n)=9a(3^(k-1))-2 if n=3^k for some k>0, a(n)=a(n-3^(k-1)) if 3^(k-1)<n<3^k for some k>0. This recursion formula has been verified for n<=2000.
a(n) = A066443(A007949(n)). (This is equivalent to the conjectured recursion above; that recursion is correct.) - Franklin T. Adams-Watters, Jul 24 2006
G.f. g(x) satisfies g(x) = 9 g(x^3) + x*(1+2*x)/(1+x+x^2). - Robert Israel, Nov 06 2016
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MAPLE
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A037314[0]:= 0;
for n from 0 to 33 do for k from 0 to 2 do
A037314[3*n+k]:= 9*A037314[n]+k
od od:
seq(A037314[i]-A037314[i-1], i=1..100); # Robert Israel, Nov 06 2016
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MATHEMATICA
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Differences@ Table[FromDigits[RealDigits[n, 3], 9], {n, 1, 100}] (* Michael De Vlieger, Nov 10 2016, after Clark Kimberling at A037314 *)
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PROG
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(PARI) a037314(n) = {my(d = digits(n, 3)); subst(Pol(d), x, 9); }
a(n) = a037314(n) - a037314(n-1); \\ Michel Marcus, Oct 30 2016
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CROSSREFS
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Cf. A000695, A007949, A037314, A066443.
Sequence in context: A102421 A019620 A105395 * A336459 A174095 A305607
Adjacent sequences: A120434 A120435 A120436 * A120438 A120439 A120440
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KEYWORD
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nonn,base
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AUTHOR
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John W. Layman, Jul 17 2006
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STATUS
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approved
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