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.

A270807 Trajectory of 1 under the map n -> n + n/gpf(n) + 1 (see A269304).

Original entry on oeis.org

1, 3, 5, 7, 9, 13, 15, 19, 21, 25, 31, 33, 37, 39, 43, 45, 55, 61, 63, 73, 75, 91, 99, 109, 111, 115, 121, 133, 141, 145, 151, 153, 163, 165, 181, 183, 187, 199, 201, 205, 211, 213, 217, 225, 271, 273, 295, 301, 309, 313, 315, 361, 381, 385, 421, 423, 433, 435, 451, 463, 465
Offset: 1

Views

Author

N. J. A. Sloane, Apr 05 2016

Keywords

Comments

Cody M. Haderlie (see A269304) conjectures that the trajectory of any initial value will eventually merge with this sequence. The trajectory of 2, for example, begins 2, 4, 7, 9, 13, 15, 19, 21, 25, ... and from 7 on coincides with this sequence. See A271418.

Crossrefs

For first differences see A270808.

Programs

  • PARI
    gpf(n) = if (n==1, 1, vecmax(factor(n)[,1]));
    lista(nn) = {a = 1; for (n=1, nn, print1(a, ", "); a = a + a/gpf(a) + 1;);} \\ Michel Marcus, Apr 06 2016
  • Python
    from _future_ import division
    from sympy import primefactors
    A270807_list, b = [], 1
    for i in range(10000):
        A270807_list.append(b)
        b += b//(max(primefactors(b)+[1])) + 1 # Chai Wah Wu, Apr 06 2016
    

A329288 Table T(n,k) read by antidiagonals: T(n,k) = f(T(n,k)) starting with T(n,1)=n, where f(x) = x - 1 + x/gpf(x), that is, f(x) = A269304(x)-2.

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 5, 5, 1, 2, 3, 5, 5, 6, 1, 2, 3, 5, 5, 7, 7, 1, 2, 3, 5, 5, 7, 7, 8, 1, 2, 3, 5, 5, 7, 7, 11, 9, 1, 2, 3, 5, 5, 7, 7, 11, 11, 10, 1, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 1, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 12
Offset: 1

Views

Author

Elijah Beregovsky, Feb 16 2020

Keywords

Comments

If p=T(n,k0) is prime, then T(n,k) = p - 1 + p/p = p for k > k0. Thus, primes are fixed points of this map. The number of different terms in the n-th row is given by A330437.

Examples

			Table begins:
   1,  1,  1,  1,  1, ...
   2,  2,  2,  2,  2, ...
   3,  3,  3,  3,  3, ...
   4,  5,  5,  5,  5, ...
   5,  5,  5,  5,  5, ...
   6,  7,  7,  7,  7, ...
   7,  7,  7,  7,  7, ...
   8, 11, 11, 11, 11, ...
   9, 11, 11, 11, 11, ...
  10, 11, 11, 11, 11, ...
  11, 11, 11, 11, 11, ...
  12, 15, 17, 17, 17, ...
  13, 13, 13, 13, 13, ...
  14, 15, 17, 17, 17, ...
		

Crossrefs

Cf. A006530 (greatest prime factor), A269304.

Programs

  • Mathematica
    Clear[f,it,order,seq]; f[n_]:=f[n]=n-1+n/FactorInteger[n][[-1]][[1]]; it[k_,n_]:=it[k,n]=f[it[k,n-1]]; it[k_,1]=k; SetAttributes[f,Listable]; SetAttributes[it,Listable]; it[#,Range[10]]&/@Range[800]

A271418 Define a sequence by b(1) = n, b(m) = b(m-1) + b(m-1)/A052126(m) + 1; then a(n) is the least m such that b(m) belongs to A270807.

Original entry on oeis.org

1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 4, 1, 2, 3, 4, 1, 3, 1, 4, 2, 4, 1, 4, 1, 4, 4, 4, 3, 2, 2, 3, 2, 2, 1, 4, 2, 2, 2, 2, 1, 4, 1, 3, 3, 2, 3, 2, 2, 3, 2, 3, 1, 4, 1
Offset: 1

Views

Author

Cody M. Haderlie, Apr 06 2016

Keywords

Examples

			the sequence where b(1) = 2 is 2, 4, 7, 9, 13, 15, ...
7 is shared with A270807
there are 3 terms in 2, 4, 7; a(2) = 3
		

Crossrefs

Programs

  • Mathematica
    f[n_] := n + n/FactorInteger[n][[-1, 1]] + 1; s = NestList[f, 1, 10^2]; Table[Length@ NestWhileList[f, n, ! MemberQ[s, #] &], {n, 120}] (* Michael De Vlieger, Apr 08 2016 *)

Extensions

a(75) corrected by Chai Wah Wu, Apr 06 2016
Showing 1-3 of 3 results.