Francisco J. Muñoz - cp's OEIS frontend

User: Francisco J. Muñoz

Francisco J. Muñoz has authored 2 sequences.

A384427 Evil numbers that are not a multiple of any other evil number.

3, 5, 17, 23, 29, 43, 53, 71, 77, 83, 89, 101, 113, 139, 149, 163, 169, 197, 209, 257, 263, 269, 277, 281, 287, 293, 311, 317, 329, 337, 343, 347, 349, 353, 359, 373, 383, 389, 401, 407, 413, 427, 449, 461, 467, 469, 479, 503, 509, 523, 533, 547, 553, 571, 593, 599

Offset: 1

Francisco J. Muñoz, May 28 2025

Robert Israel, Table of n, a(n) for n = 1..10000

Union of A217790 and A027699.

Cf. A001969, A129771.

isevil:= proc(n) convert(convert(n,base,2),`+`)::even end proc:
N:= 1000: # for terms <= N
V:= Vector(N,1):
for i from 1 to N do
    if isevil(i) then V[[seq(j,j=2*i .. N, i)]]:= 0
    else V[i]:= 0
    fi
od:
select(t -> V[t]=1, [$1..N]); # Robert Israel, Jun 18 2025

evilQ[n_] := EvenQ[DigitCount[n, 2, 1]]; q[n_] := evilQ[n] && AllTrue[Divisors[n], # == n || ! evilQ[#] &]; Select[Range[600], q] (* Amiram Eldar, May 31 2025 *)

isevil(n) = hammingweight(n) % 2 == 0;
noevildiv(n) = {fordiv(n, d, if ((d < n) && isevil(d), return (0)); ); 1; }
isok(n) = isevil(n) && noevildiv(n); \\ Michel Marcus, May 31 2025

A333363 Horizontal visibility sequence at the onset of chaos in the 3-period cascade.

Original entry on oeis.org

3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 9, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 11, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 9, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 13, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 9, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 11, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 9, 3, 2, 5, 3, 2, 7, 3, 2, 5, 3, 2, 15

Offset: 1

Francisco J. Muñoz and Juan Carlos Nuño, Mar 16 2020

This sequence represents the horizontal visibility of the points of the chaotic time series at the onset of chaos in the 3-period cascade of the logistic (unimodal) map.

Observation: if the sequence is written as a table array with six columns read by rows we have that, at least for the first 16 rows, the n-th row is "3, 2, 5, 3, 2" together with (6 + A037227(n)), see the example. - Omar E. Pol, Mar 16 2020

			From _Omar E. Pol_, Mar 16 2020: (Start)
Written as a table with six columns read by rows:
  3, 2, 5, 3, 2,  7;
  3, 2, 5, 3, 2,  9;
  3, 2, 5, 3, 2,  7;
  3, 2, 5, 3, 2, 11;
  3, 2, 5, 3, 2,  7;
  3, 2, 5, 3, 2,  9;
  3, 2, 5, 3, 2,  7;
  3, 2, 5, 3, 2, 13;
  3, 2, 5, 3, 2,  7;
  3, 2, 5, 3, 2,  9;
  3, 2, 5, 3, 2,  7;
  3, 2, 5, 3, 2, 11;
  3, 2, 5, 3, 2,  7;
  3, 2, 5, 3, 2,  9;
  3, 2, 5, 3, 2,  7;
  3, 2, 5, 3, 2, 15;
(End)

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Juan C. Nuño and Francisco J. Muñoz, Universal visibility patterns of unimodal maps, arXiv:2002.10423 [nlin.CD], 2020.
Juan C. Nuño and Francisco J. Muñoz, Universal visibility patterns of unimodal maps, Chaos, 30, 063105 (2020).
Juan Carlos Nuño and Francisco J. Muñoz, On the ubiquity of the ruler sequence, arXiv:2009.14629 [math.HO], 2020.
Juan Carlos Nuño and Francisco J. Muñoz, The Ruler Sequence Revisited: A Dynamic Perspective, Mathematics (2024) Vol. 12, No. 5, 742.

Cf. A007814, A037227.

L[n_] := L[n] = Block[{s = {3, 2, 2*n+3}}, Do[s = Join[L[i], s], {i, n-1}]; s]; L[6] (* Giovanni Resta, Mar 16 2020 *)

visibsuc3 <- function(n){
    suc <- c(3,2, 2*(n+1)+1)
    if(n>1){
    for(i in 1:(n-1)){
    suc <- c(visibsuc3(i), suc)
    }
   }
   return(suc)
  }

Conjectured: a(n) = 2*A007814(n/3) + 5 if 3|n and a(n) = 4 - (n mod 3) otherwise. - Giovanni Resta, Mar 16 2020

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User: Francisco J. Muñoz

A384427 Evil numbers that are not a multiple of any other evil number.

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