A088226 -id:A088226 - cp's OEIS frontend

A077623 a(1)=1, a(2)=2, a(3)=4, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

1, 2, 4, 1, 5, 0, 6, 1, 5, 2, 4, 3, 3, 4, 2, 5, 1, 6, 0, 7, 1, 6, 2, 5, 3, 4, 4, 3, 5, 2, 6, 1, 7, 0, 8, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 6, 2, 7, 1, 8, 0, 9, 1, 8, 2, 7, 3, 6, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 9, 0, 10, 1, 9, 2, 8, 3, 7, 4, 6, 5, 5, 6, 4, 7, 3, 8, 2, 9, 1, 10, 0, 11, 1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 6

Offset: 1

Benoit Cloitre, Dec 02 2002

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A077653, A079623, A079624, A080096, A088226.

a077623 n = a077623_list !! (n-1)
a077623_list = 1 : 2 : 4 : zipWith3 (\u v w -> abs (w - v - u))
               a077623_list (tail a077623_list) (drop 2 a077623_list)
-- Reinhard Zumkeller, Oct 11 2014

m:=120;
A077623:=[n le 3 select 2^(n-1) else Abs(Self(n-1) - Self(n-2) - Self(n-3)): n in [1..m+5]];
[A077623[n]: n in [1..m]]; // G. C. Greubel, Sep 11 2024

a[n_]:= a[n]= If[n<4, 2^(n-1), Abs[a[n-1] -a[n-2] -a[n-3]]];
Table[a[n], {n,120}] (* G. C. Greubel, Sep 11 2024 *)

@CachedFunction
def a(n): # a = A077623
    if n<4: return 2^(n-1)
    else: return abs(a(n-1)-a(n-2)-a(n-3))
[a(n) for n in range(1,121)] # G. C. Greubel, Sep 11 2024

a(n)/sqrt(n) is bounded. More precisely, let M(n) = Max ( a(k) : 1<=k<=n ); then M(n) = floor(sqrt(n+29)) for n>=4

A080096 a(1) = a(2) = 1, a(3) = 2, thereafter a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

Original entry on oeis.org

1, 1, 2, 0, 3, 1, 2, 2, 1, 3, 0, 4, 1, 3, 2, 2, 3, 1, 4, 0, 5, 1, 4, 2, 3, 3, 2, 4, 1, 5, 0, 6, 1, 5, 2, 4, 3, 3, 4, 2, 5, 1, 6, 0, 7, 1, 6, 2, 5, 3, 4, 4, 3, 5, 2, 6, 1, 7, 0, 8, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 6, 2, 7, 1, 8, 0, 9, 1, 8, 2, 7, 3, 6, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 9, 0, 10, 1, 9, 2, 8, 3, 7, 4, 6, 5

Offset: 1

Benoit Cloitre, Jan 28 2003

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A028347, A028557, A077623, A077653, A079623, A079624, A088226.

a080096 n = a080096_list !! (n-1)
a080096_list = 1 : 1 : 2 : zipWith3 (\u v w -> abs (w - v - u))
               a080096_list (tail a080096_list) (drop 2 a080096_list)
-- Reinhard Zumkeller, Oct 11 2014

m:=120;
A080096:=[n le 3 select Floor((n+1)/2) else Abs(Self(n-1) - Self(n-2) - Self(n-3)): n in [1..m+5]];
[A080096[n]: n in [1..m]]; // G. C. Greubel, Sep 11 2024

nxt[{a_,b_,c_}]:={b,c,Abs[c-b-a]}; NestList[nxt,{1,1,2},110][[All,1]] (* Harvey P. Dale, Nov 14 2021 *)

a(n)=local(k,m); if(n<1,0,k=sqrtint(n+4); m=n+4-k^2; if(m%2,m\2+1,k-m\2))

@CachedFunction
def a(n): # a = A080096
    if n<4: return int((n+1)//2)
    else: return abs(a(n-1)-a(n-2)-a(n-3))
[a(n) for n in range(1,101)] # G. C. Greubel, Sep 11 2024

For n>=3 Max( a(k) : 1<=k<=n ) = floor ( sqrt(n+4)).
Special cases: a(n^2 + 4*n - 1) = 0 and a(n^2 - 4) = n.
a(A028557(n)) = a(A028557(n+1)).
Sum_{k=(n-1)^2 .. n^2} a(k) = n^2.

A077653 a(1)=1, a(2)=2, a(3)=2, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

Original entry on oeis.org

1, 2, 2, 1, 3, 0, 4, 1, 3, 2, 2, 3, 1, 4, 0, 5, 1, 4, 2, 3, 3, 2, 4, 1, 5, 0, 6, 1, 5, 2, 4, 3, 3, 4, 2, 5, 1, 6, 0, 7, 1, 6, 2, 5, 3, 4, 4, 3, 5, 2, 6, 1, 7, 0, 8, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 6, 2, 7, 1, 8, 0, 9, 1, 8, 2, 7, 3, 6, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 9, 0, 10, 1, 9, 2, 8, 3, 7, 4, 6, 5, 5, 6, 4, 7

Offset: 1

Benoit Cloitre, Dec 02 2002

nonn

Conjecture : let z(1)=x; z(2)=y; z(3)= z; z(n)=abs(z(n-1)-z(n-2)-z(n-3)) if z(n) is unbounded (i.e. x,y,z are such that z(n) doesn't reach a cycle of length 2), then there are 2 integers n(x,y,z) and w(x,y,z) such that M(n) = floor(sqrt(n+w(x,y,z))) for n>n(,x,y,z) where M(n) = Max ( a(k) : 1<=k<=n ). As example : w(1,2,2)=9 n(1,2,2)=4; w(1,2,4)=29 n(1,2,4)=4; w(1,2,8)=157 n(1,2,8)=9

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A077623, A079623, A079624, A080096, A088226.

a077653 n = a077653_list !! (n-1)
a077653_list = 1 : 2 : 2 : zipWith3 (\u v w -> abs (w - v - u))
               a077653_list (tail a077653_list) (drop 2 a077653_list)
-- Reinhard Zumkeller, Oct 11 2014

m:=120;
A077653:=[n le 3 select Floor((n+2)/2) else Abs(Self(n-1) - Self(n-2) - Self(n-3)): n in [1..m+5]];
[A077653[n]: n in [1..m]]; // G. C. Greubel, Sep 11 2024

nxt[{a_,b_,c_}]:={b,c,Abs[c-b-a]}; NestList[nxt,{1,2,2},110][[All,1]] (* Harvey P. Dale, Sep 01 2020 *)

@CachedFunction
def a(n): # a = A077653
    if n<4: return int((n+2)//2)
    else: return abs(a(n-1)-a(n-2)-a(n-3))
[a(n) for n in range(1,101)] # G. C. Greubel, Sep 11 2024

a(n)/sqrt(n) is bounded. More precisely, let M(n) = Max ( a(k) : 1<=k<=n ); then M(n)= floor(sqrt(n+9)) for n>4

A079623 a(1) = a(2) = 1, a(3)=4, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

Original entry on oeis.org

1, 1, 4, 2, 3, 3, 2, 4, 1, 5, 0, 6, 1, 5, 2, 4, 3, 3, 4, 2, 5, 1, 6, 0, 7, 1, 6, 2, 5, 3, 4, 4, 3, 5, 2, 6, 1, 7, 0, 8, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 6, 2, 7, 1, 8, 0, 9, 1, 8, 2, 7, 3, 6, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 9, 0, 10, 1, 9, 2, 8, 3, 7, 4, 6, 5, 5, 6, 4, 7, 3, 8, 2, 9, 1, 10, 0, 11, 1, 10, 2, 9, 3, 8

Offset: 1

Benoit Cloitre, Jan 30 2003

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A077623, A077653, A078108, A079624, A080096, A088226.

a079623 n = a079623_list !! (n-1)
a079623_list = 1 : 1 : 4 : zipWith3 (\u v w -> abs (w - v - u))
               a079623_list (tail a079623_list) (drop 2 a079623_list)
-- Reinhard Zumkeller, Oct 11 2014

m:=120;
A079623:=[n le 3 select 4^Floor((n-1)/2) else Abs(Self(n-1) - Self(n-2) - Self(n-3)): n in [1..m+5]];
[A079623[n]: n in [1..m]]; // G. C. Greubel, Sep 11 2024

nxt[{a_,b_,c_}]:={b,c,Abs[c-b-a]}; NestList[nxt,{1,1,4},110][[All,1]] (* Harvey P. Dale, Aug 12 2020 *)

@CachedFunction
def a(n): # a = A079623
    if n<4: return 4^((n-1)//2)
    else: return abs(a(n-1)-a(n-2)-a(n-3))
[a(n) for n in range(1,101)] # G. C. Greubel, Sep 11 2024

a(n*(n-10)) = 0.

Max( a(k) : 1<=k<=n) = floor(sqrt(n+24)).

A079624 a(1) = a(2) = 1, a(3) = 6, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

Original entry on oeis.org

1, 1, 6, 4, 3, 7, 0, 10, 3, 7, 6, 4, 9, 1, 12, 2, 11, 3, 10, 4, 9, 5, 8, 6, 7, 7, 6, 8, 5, 9, 4, 10, 3, 11, 2, 12, 1, 13, 0, 14, 1, 13, 2, 12, 3, 11, 4, 10, 5, 9, 6, 8, 7, 7, 8, 6, 9, 5, 10, 4, 11, 3, 12, 2, 13, 1, 14, 0, 15, 1, 14, 2, 13, 3, 12, 4, 11, 5, 10, 6, 9, 7, 8, 8, 7, 9, 6, 10, 5, 11, 4, 12, 3

Offset: 1

Benoit Cloitre, Jan 30 2003

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A077623, A077653, A078108, A079623, A080096, A088226.

a079624 n = a079624_list !! (n-1)
a079624_list = 1 : 1 : 6 : zipWith3 (\u v w -> abs (w - v - u))
               a079624_list (tail a079624_list) (drop 2 a079624_list)
-- Reinhard Zumkeller, Oct 11 2014

m:=120;
A079624:=[n le 3 select 6^Floor((n-1)/2) else Abs(Self(n-1) - Self(n-2) - Self(n-3)): n in [1..m+5]];
[A079624[n]: n in [1..m]]; // G. C. Greubel, Sep 11 2024

a[n_]:= a[n]= If[n<4, 6^Floor[(n-1)/2], Abs[a[n-1] -a[n-2] -a[n-3]]];
Table[a[n], {n,100}] (* G. C. Greubel, Sep 11 2024 *)

@CachedFunction
def a(n): # a = A079624
    if n<4: return 6^((n-1)//2)
    else: return abs(a(n-1)-a(n-2)-a(n-3))
[a(n) for n in range(1,101)] # G. C. Greubel, Sep 11 2024

For n >= 5, a(n^2 + 24*n - 13) = 0.

For n >= 38, Max( a(k) : 1<=k<=n) = floor(sqrt(n+156)).

cp's OEIS Frontend

A077623 a(1)=1, a(2)=2, a(3)=4, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

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A080096 a(1) = a(2) = 1, a(3) = 2, thereafter a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

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A077653 a(1)=1, a(2)=2, a(3)=2, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

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A079623 a(1) = a(2) = 1, a(3)=4, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

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Programs

Haskell

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Mathematica

SageMath

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A079624 a(1) = a(2) = 1, a(3) = 6, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Magma

Mathematica

SageMath

Formula