A093349 -id:A093349 - cp's OEIS frontend

A094117 Partial sums of A093349.

0, 1, 1, 2, 2, 3, 3, 10, 16, 23, 29, 36, 42, 49, 49, 50, 50, 51, 51, 52, 52, 59, 65, 72, 78, 85, 91, 98, 98, 99, 99, 100, 100, 101, 101, 108, 114, 121, 127, 134, 140, 147, 147, 148, 148, 149, 149, 150, 150, 199, 247, 296, 344, 393, 441, 490, 532, 575, 617, 660, 702, 745

Offset: 1

Benoit Cloitre, May 03 2004

nonn

a(n)=sum(k=1,n,-sum(i=1,k-1,(-1)^i*7^valuation(i,7)))

a(7^k)=(49^k-1)/16

A093347 A 3-fractal "castle" starting with 0.

Original entry on oeis.org

0, 1, 0, 3, 2, 3, 0, 1, 0, 9, 8, 9, 6, 7, 6, 9, 8, 9, 0, 1, 0, 3, 2, 3, 0, 1, 0, 27, 26, 27, 24, 25, 24, 27, 26, 27, 18, 19, 18, 21, 20, 21, 18, 19, 18, 27, 26, 27, 24, 25, 24, 27, 26, 27, 0, 1, 0, 3, 2, 3, 0, 1, 0, 9, 8, 9, 6, 7, 6, 9, 8, 9, 0, 1, 0, 3, 2, 3, 0, 1, 0, 81, 80, 81, 78, 79, 78, 81

Offset: 1

Benoit Cloitre, Apr 26 2004

Amiram Eldar, Table of n, a(n) for n = 1..10000
Benoit Cloitre, Graph of a(n) for n=1 up to 9
Benoit Cloitre, Graph of a(n) for n=1 up to 27
Benoit Cloitre, Graph of a(n) for n=1 up to 81
Benoit Cloitre, Graph of a(n) for n=1 up to 243

Cf. A093348, A093349

Cf. A038500.

a[n_] := Sum[(-1)^(i+1) * 3^IntegerExponent[i, 3], {i, 1, n-1}]; Array[a, 100] (* Amiram Eldar, Jun 17 2022 *)

a(n)=if(n<2,0,3^floor(log(n-1)/log(3))-a(n-3^floor(log(n-1)/log(3))))

a(n) = my(s=-1); fromdigits([if(d==1,s=-s) |d<-digits(n-1,3)], 3); \\ Kevin Ryde, Jan 01 2024

a(1) = 0 then a(n) = w(n) - a(n-w(n)) where w(n) = 3^floor(log(n-1)/log(3)).
a(3^n) = 0, a(3^n+1) = 3^n, a(3^n+2) = 3^n-1, a(3^n+3) = 3^n, etc.
a(n) = Sum_{i=1..n-1} (-1)^(i-1)*3^valuation(i, 3).

A093348 A 5-fractal "castle" starting with 0.

Original entry on oeis.org

0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 25, 24, 25, 24, 25, 20, 21, 20, 21, 20, 25, 24, 25, 24, 25, 20, 21, 20, 21, 20, 25, 24, 25, 24, 25, 0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 25, 24, 25, 24, 25, 20, 21, 20, 21, 20, 25, 24

Offset: 1

Benoit Cloitre, Apr 26 2004

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000
Benoit Cloitre, Graph of a(n) for n=1 up to 25
Benoit Cloitre, Graph of a(n) for n=1 up to 125
Benoit Cloitre, Graph of a(n) for n=1 up to 625

Cf. A093347, A093349.

Cf. A060904.

a[n_] := Sum[(-1)^(i+1) * 5^IntegerExponent[i, 5], {i, 1, n-1}]; Array[a, 100] (* Amiram Eldar, Jun 17 2022 *)

a(n)=if(n<2,0,5^floor(log(n-1)/log(5))-a(n-5^floor(log(n-1)/log(5))))

a(1) = 0, then a(n) = w(n) - a(n-w(n)) where w(n) = 5^floor(log(n-1)/log(5)).
a(n) = Sum_{i=1..n-1} (-1)^(i-1)*5^valuation(i, 5).
Conjecture: a(n+1) = (n mod 2) + Sum_{k=0..infinity} (4*5^k*(floor(n/5^(k+1)) mod 2)). - Charlie Neder, May 25 2019

cp's OEIS Frontend

A094117 Partial sums of A093349.

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A093347 A 3-fractal "castle" starting with 0.

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A093348 A 5-fractal "castle" starting with 0.

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