cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A175723 a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)), where gpf = "greatest prime factor".

Original entry on oeis.org

1, 1, 2, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5
Offset: 1

Views

Author

N. J. A. Sloane, Dec 16 2010

Keywords

Comments

Rapidly enters a loop with period 3,5,2,7.
More generally, if a(1) and a(2) are distinct positive numbers with a(1)+a(2) >= 2, the sequence eventually enters the cycle {7,3,5,2} [Back and Caragiu].

Links

Crossrefs

Cf. A000045, A006530, A020639.
Similar or related sequences: A177904, A177923, A178094, A178095, A178174, A178179, A180101, A180107, A221183.

Programs

  • Mathematica
    nxt[{a_,b_}]:={b,FactorInteger[a+b][[-1,1]]}; Transpose[NestList[nxt,{1,1},120]][[1]] (* or *) PadRight[{1,1,2},130,{5,2,7,3}] (* Harvey P. Dale, Feb 24 2015 *)

A177904 a(1)=a(2)=a(3)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)+a(n-3)), where gpf = "greatest prime factor".

Original entry on oeis.org

1, 1, 1, 3, 5, 3, 11, 19, 11, 41, 71, 41, 17, 43, 101, 23, 167, 97, 41, 61, 199, 43, 101, 7, 151, 37, 13, 67, 13, 31, 37, 3, 71, 37, 37, 29, 103, 13, 29, 29, 71, 43, 13, 127, 61, 67, 17, 29, 113, 53, 13, 179, 7, 199, 11, 31, 241, 283, 37, 17, 337, 23, 29, 389, 7, 17, 59, 83, 53, 13, 149, 43, 41, 233, 317, 197, 83, 199, 479, 761, 1439, 47, 107
Offset: 1

Views

Author

N. J. A. Sloane, Dec 16 2010

Keywords

Comments

After 86 steps, enters a cycle of length 212 (see A177923).

Links

Crossrefs

Cf. A006530, A175723, A178174, A178095, A214320.

Programs

  • Haskell
    a177904 n = a177904_list !! (n-1)
a177904_list = 1 : 1 : 1 : (map a006530 $ zipWith (+)
   a177904_list (tail $ zipWith (+) a177904_list $ tail a177904_list))
-- Reinhard Zumkeller, Jul 24 2012
  • Maple
    with(numtheory, divisors); A006530 := proc(n) local i, t1, t2, t3, t4, t5; t1 := divisors(n); t2 := convert(t1, list); t3 := sort(t2); t4 := nops(t3); t5 := 1; for i from 1 to t4 do if isprime(t3[t4+1-i]) then RETURN(t3[t4+1-i]); fi; od; 1; end;
M:=1000;
t1:=[1,1,1];
for n from 4 to M do
t1:=[op(t1),A006530(t1[n-1]+t1[n-2]+t1[n-3])]; od:
t1;
  • Mathematica
    nxt[{a_,b_,c_}]:={b,c,FactorInteger[a+b+c][[-1,1]]}; NestList[nxt,{1,1,1},90][[All,1]] (* Harvey P. Dale, Jul 17 2017 *)

A178094 a(1)=a(2)=1; thereafter a(n) = lpf(a(n-1)+a(n-2)), where lpf = "least prime factor".

Original entry on oeis.org

1, 1, 2, 3, 5, 2, 7, 3, 2, 5, 7, 2, 3, 5, 2, 7, 3, 2, 5, 7, 2, 3, 5, 2, 7, 3, 2, 5, 7, 2, 3, 5, 2, 7, 3, 2, 5, 7, 2, 3, 5, 2, 7, 3, 2, 5, 7, 2, 3, 5, 2, 7, 3, 2, 5, 7, 2, 3, 5, 2, 7, 3, 2, 5, 7, 2, 3, 5, 2, 7, 3, 2, 5, 7, 2, 3, 5, 2, 7, 3, 2, 5, 7, 2, 3, 5, 2, 7, 3, 2, 5, 7, 2, 3, 5, 2, 7, 3, 2, 5, 7, 2, 3, 5, 2, 7, 3, 2, 5, 7
Offset: 1

Views

Author

N. J. A. Sloane, Dec 16 2010

Keywords

Comments

Cycles with a period of length 9.

Crossrefs

Cf. A000045, A175723, A020639, A178095.

Programs

  • Mathematica
    nxt[{a_,b_}]:={b,FactorInteger[a+b][[1,1]]}; NestList[nxt,{1,1},110][[;;,1]] (* or *) PadRight[ {1,1},110,{5,7,2,3,5,2,7,3,2}] (* Harvey P. Dale, May 29 2023 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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