A350313 -id:A350313 - cp's OEIS frontend

A350314 The catch-up points of the Redstone permutation A350313.

2, 5, 11, 17, 23, 29, 37, 41, 47, 53, 59, 67, 71, 77, 83, 89, 97, 101, 107, 113, 119, 127, 131, 137, 143, 149, 157, 161, 167, 173, 179, 187, 191, 197, 203, 209, 221, 227, 233, 239, 247, 251, 257, 263, 269, 277, 281, 287, 293, 299, 307, 311, 317, 323, 329, 337

Offset: 1

Peter Luschny, Dec 24 2021

nonn

We say n is a 'catch-up point' of a permutation p of the positive integers if and only if p restricted to [n] = {1, 2, ..., n} is a permutation of [n].

The periodic structure of the first differences is described in A350315.

Cf. A350313, A350315.

s = {2, 1}; c[] = 0; Array[Set[c[s[[#]]], #] &, Length[s]]; j = Last[s]; u = 3; {2}~Join~Reap[Monitor[Do[If[j == u, While[c[u] > 0, u++]]; k = u; While[Nand[c[k] == 0, CoprimeQ[i, k], ! Divisible[i - 1, k]], k++]; If[k == u, Sow[i]]; Set[c[k], i]; j = k, {i, Length[s] + 1, 337}], i]][[-1, -1]] (* _Michael De Vlieger, Dec 24 2021 *)

A350315 Length of the rows of the Redstone permutation A350313.

Original entry on oeis.org

2, 3, 6, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4, 6, 6, 6, 12, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4, 6, 6, 6, 12, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4, 6, 6, 6, 8, 4

Offset: 1

Peter Luschny, Dec 24 2021

nonn

See the comments and the example section of A350313 for definitions.

Cf. A350313, A350314.

s = {2, 1}; c[] = 0; Array[Set[c[s[[#]]], #] &, Length[s]]; j = Last[s]; u = 3; Prepend[Differences[#], First[#]] &[{2}~Join~Reap[Monitor[Do[If[j == u, While[c[u] > 0, u++]]; k = u; While[Nand[c[k] == 0, CoprimeQ[i, k], ! Divisible[i - 1, k]], k++]; If[k == u, Sow[i]]; Set[c[k], i]; j = k, {i, Length[s] + 1, 500}], i]][[-1, -1]]] (* _Michael De Vlieger, Dec 24 2021 *)

Apparently for n >= 4: a(n) = 2 * b(n - 4) + 6, where the generating function of b(n) is (-3*x^33 + x^29 - x^28 + x^24 - x^23 + x^19 - x^18 + x^14 - x^13 + x^9 - x^8 + x^4 - x^3)/(x^34 - 1).

cp's OEIS Frontend

A350314 The catch-up points of the Redstone permutation A350313.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica