A305865 -id:A305865 - cp's OEIS frontend

A318265 a(1) = 1, a(n) = 5*a(n/3) if n is divisible by 3, otherwise a(n) = n - a(n-1).

1, 1, 5, -1, 6, 5, 2, 6, 25, -15, 26, -5, 18, -4, 30, -14, 31, 25, -6, 26, 10, 12, 11, 30, -5, 31, 125, -97, 126, -75, 106, -74, 130, -96, 131, -25, 62, -24, 90, -50, 91, -20, 63, -19, 150, -104, 151, -70, 119, -69, 155, -103, 156, 125, -70, 126, -30, 88, -29, 130, -69, 131, 50, 14, 51, 60, 7, 61, 55, 15, 56, 150

Offset: 1

Altug Alkan and Antti Karttunen, Aug 22 2018

From a generalization of A317825.

Antti Karttunen, Table of n, a(n) for n = 1..19682
Altug Alkan, A scatterplot of a(n) for n <= 3^10-1
Rémy Sigrist, A colored scatterplot of (A318265(n), A305865(n)) for n = 1..3^13-1 (color is function of n)

Cf. A305865, A317825.

a(n)=if(n==1, n, if(n%3==0, 5*a(n/3),n-a(n-1)));

A318303 a(0) = 0, a(n) = n + a(n-1) if n is odd, a(n) = -3*a(n/2) if n is even.

Original entry on oeis.org

0, 1, -3, 0, 9, 14, 0, 7, -27, -18, -42, -31, 0, 13, -21, -6, 81, 98, 54, 73, 126, 147, 93, 116, 0, 25, -39, -12, 63, 92, 18, 49, -243, -210, -294, -259, -162, -125, -219, -180, -378, -337, -441, -398, -279, -234, -348, -301, 0, 49, -75, -24, 117, 170, 36, 91, -189, -132, -276, -217, -54, 7, -147, -84, 729, 794, 630

Offset: 0

Altug Alkan, Aug 24 2018

Let g_k(0) = 0. g_k(n) = n + g_k(n-1) if n is odd, g_k(n) = k*a(n/2) if n is even. A228451(n) is g_1(n), A298011(n) is g_2(n). This sequence is a(n) = g_k(n) where k = -3.

Altug Alkan, Table of n, a(n) for n = 0..32767
Rémy Sigrist, Colored scatterplot of a(n) for n = 0..1000000 (where the color is function of A262304(n))
Rémy Sigrist, Colored scatterplot of a(n) for n = 0..1000000 (where the color is function of floor(n / 2^(A070939(n) - 6)))
Rémy Sigrist, A colored scatterplot of (A317825(n), abs(A318303(n))) for n = 1..2^20-1 (where the color is function of floor(n / 2^(A070939(n)-5)))
Altug Alkan, A scatterplot of (A317825(n), A318303(n)+A317825(n)) for n = 1..2^17-1

Cf. A070939, A228451, A262304, A298011, A305865, A317825, A318265.

Nest[Append[#1, If[OddQ@ #2, #2 + #1[[-1]], -3 #1[[#2/2 + 1]] ]] & @@ {#, Length@ #} &, {0}, 66] (* Michael De Vlieger, Aug 25 2018 *)

a(n)=if(n==0, 0, if(n%2, n+a(n-1), -3*a(n/2)));

A318553 a(1) = 1, a(n) = -5*a(n/3) if n is divisible by 3, a(n) = n - a(n-1) if n + 1 is divisible by 3, otherwise a(n) = n + a(n-1).

Original entry on oeis.org

1, 1, -5, -1, 6, -5, 2, 6, 25, 35, -24, 5, 18, -4, -30, -14, 31, 25, 44, -24, -10, 12, 11, -30, -5, 31, -125, -97, 126, -175, -144, 176, 120, 154, -119, -25, 12, 26, -90, -50, 91, 20, 63, -19, 150, 196, -149, 70, 119, -69, -155, -103, 156, -125, -70, 126, -220, -162, 221, 120, 181, -119, 50, 114, -49, -60, 7, 61

Offset: 1

Altug Alkan, Aug 28 2018

Altug Alkan, Table of n, a(n) for n = 1..10934
Altug Alkan, A scatterplot of a(n) for 4*3^8 <= n <= 5*3^8-1

Cf. A305865.

a[1]=1; a[n_] := a[n] = Switch[Mod[n, 3], 0, -5 a[n/3], 1, n + a[n-1], 2, n - a[n-1]]; Array[a, 68] (* Giovanni Resta, Sep 05 2018 *)

a = vector(99); for(n=1, #a, print1 (a[n]=if(n<=1, 1, if (n%3==0, -5*a[n/3],if(n%3==1, n+a[n-1],n-a[n-1])))", "));

a(n) = if(n==1, 1, if(n%3==0, -5*a(n/3), if(n%3==1, n+a(n-1), n-a(n-1))))

cp's OEIS Frontend

A318265 a(1) = 1, a(n) = 5*a(n/3) if n is divisible by 3, otherwise a(n) = n - a(n-1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A318303 a(0) = 0, a(n) = n + a(n-1) if n is odd, a(n) = -3*a(n/2) if n is even.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

A318553 a(1) = 1, a(n) = -5*a(n/3) if n is divisible by 3, a(n) = n - a(n-1) if n + 1 is divisible by 3, otherwise a(n) = n + a(n-1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI