Search: a238270 -id:a238270
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A238271
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Decimal expansion of sum(n>=1, mu(n)/3^n ).
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+10
5
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1, 8, 1, 9, 9, 5, 3, 8, 6, 7, 0, 2, 6, 3, 3, 8, 8, 7, 8, 2, 7, 8, 0, 0, 1, 0, 0, 3, 0, 0, 5, 6, 5, 5, 7, 3, 2, 2, 6, 3, 4, 4, 9, 8, 0, 1, 3, 5, 3, 8, 3, 0, 6, 1, 7, 5, 9, 2, 4, 9, 4, 7, 7, 1, 6, 3, 2, 4, 2, 0, 4, 8, 3, 6, 8, 5, 0, 5, 4, 1, 6, 4, 2, 2, 8, 9, 8, 3, 9, 5, 7, 7, 6, 4, 9, 2, 3, 9, 9, 0, 2, 6, 9, 9, 4
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OFFSET
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0,2
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COMMENTS
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Suggested by a posting to SeqFan list by Alonso Del Arte at 15:35 on Aug 09 2012.
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LINKS
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EXAMPLE
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=0.1819953867026338878278001003005655732263449801353830617592494771...
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MATHEMATICA
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RealDigits[ Sum[ N[ MoebiusMu[n] 3^-n, 128], {n, 300}], 10, 111][[1]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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A344432
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a(n) = Sum_{k=1..n} mu(k) * 2^(n - k).
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+10
5
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0, 1, 1, 1, 2, 3, 7, 13, 26, 52, 105, 209, 418, 835, 1671, 3343, 6686, 13371, 26742, 53483, 106966, 213933, 427867, 855733, 1711466, 3422932, 6845865, 13691730, 27383460, 54766919, 109533837, 219067673, 438135346, 876270693, 1752541387, 3505082775, 7010165550
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: (Sum_{k>=1} mu(k) * x^k) / (1 - 2*x).
a(n) = 2 * a(n-1) + mu(n) for n > 0.
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MATHEMATICA
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a[n_] := Sum[MoebiusMu[k] * 2^(n-k), {k, 1, n}]; Array[a, 40] (* Amiram Eldar, May 19 2021 *)
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PROG
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(PARI) a(n) = sum(k=1, n, moebius(k)*2^(n-k));
(PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, moebius(k)*x^k)/(1-2*x)))
(PARI) a(n) = if(n==0, 0, 2*a(n-1)+moebius(n));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A181673
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Decimal expansion of Sum_{n>=1} moebius(n)*(1/10)^n.
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+10
4
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0, 8, 8, 9, 9, 0, 9, 0, 0, 0, 8, 9, 9, 1, 0, 9, 8, 9, 9, 0, 1, 0, 9, 0, 0, 0, 9, 9, 8, 8, 9, 0, 1, 1, 0, 9, 9, 1, 0, 9, 8, 8, 9, 0, 0, 0, 9, 0, 0, 0, 0, 9, 9, 0, 1, 0, 1, 0, 8, 9, 9, 1, 0, 0, 0, 8, 9, 0, 0, 8, 8, 9, 9, 1, 0, 0, 0, 8, 9, 0, 0, 0, 9, 0, 1, 1, 0, 9, 9
(list;
constant;
graph;
refs;
listen;
history;
text;
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OFFSET
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0,2
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LINKS
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EXAMPLE
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0.088990900089910989901090009988901109910...
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MATHEMATICA
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RealDigits[ Sum[ N[ MoebiusMu[n] 10^-n, 128], {n, 120}], 10, 111][[1]] (* Robert G. Wilson v, Feb 21 2014 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A238273
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Decimal expansion of the sum(n>=1, mu(n)/n^n ) where mu is the Moebius function.
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+10
3
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7, 1, 2, 6, 6, 3, 1, 8, 2, 2, 6, 4, 2, 8, 3, 4, 5, 7, 1, 2, 1, 6, 0, 4, 1, 6, 8, 3, 2, 1, 8, 6, 1, 2, 5, 0, 6, 0, 5, 3, 0, 7, 0, 2, 1, 7, 4, 7, 1, 6, 1, 3, 6, 9, 0, 7, 0, 3, 5, 0, 5, 0, 6, 3, 2, 9, 5, 5, 5, 6, 6, 1, 2, 1, 0, 4, 4, 7, 0, 6, 1, 4, 3, 6, 4, 1, 1, 4, 6, 2, 7, 0, 5, 9, 4, 3, 6, 2, 7, 6, 2, 1, 6, 0, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Suggested by a posting to SeqFan list by Alonso Del Arte at 15:35 on Aug 09 2012.
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LINKS
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EXAMPLE
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=.71266318226428345712160416832186125060530702174716136907035050632955566121...
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MATHEMATICA
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RealDigits[ Sum[ N[ MoebiusMu[n] 1 n^-n, 128], {n, 100}], 10, 111][[1]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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