A078108 -id:A078108 - cp's OEIS frontend

A078109 Let u(1)=u(2)=1, u(3)=2n, u(k) = abs(u(k-1)-u(k-2)-u(k-3)) and M(k) = Max_{1<=i<=k} u(i), then for any k >= a(n), M(k) = floor(sqrt(k + A078108(n))).

3, 10, 38, 10, 35, 66, 19, 150, 90, 30, 243, 159, 138, 270, 19, 186, 35, 178, 358, 127, 46, 334, 123, 370, 438, 343, 182, 430, 46, 454, 470, 534, 30, 618, 734, 903, 570, 302, 571, 638, 30, 166, 822, 647, 426, 998, 75, 106, 606, 322, 82, 210, 1798, 330, 506

Offset: 1

Benoit Cloitre, Dec 05 2002

nonn

Conjecture : a(n) always exists, a(n)/n^2 is bounded. If initial conditions are u(1)=u(2)=1, u(3)=2n+1, then u(k) reaches a 2-cycle for any k>m large enough (cf. A078098)

Cf. A000196, A078108, A077623.

Typos in data corrected and more terms from Sean A. Irvine, Jun 16 2025

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

A078109 Let u(1)=u(2)=1, u(3)=2n, u(k) = abs(u(k-1)-u(k-2)-u(k-3)) and M(k) = Max_{1<=i<=k} u(i), then for any k >= a(n), M(k) = floor(sqrt(k + A078108(n))).

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

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Author

Keywords

Links

Crossrefs

Programs

Haskell

Magma

Mathematica

SageMath

Formula