A362241 Binary encoding of the rows of A362240.

0, 1, 0, 3, 0, 5, 7, 0, 10, 13, 0, 3, 4, 7, 14, 31, 4, 9, 13, 15, 17, 20, 27, 28, 37, 44, 51, 53, 63, 2, 15, 17, 20, 28, 31, 41, 44, 46, 48, 53, 58, 71, 78, 99, 101, 123, 2, 5, 7, 11, 17, 19, 24, 35, 39, 41, 55, 58, 63, 72, 83, 85, 89, 97, 107, 111, 113, 134

Offset

1,4

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Samuel Harkness, MATLAB program

Neal Gersh Tolunsky, Scatterplot of a(n) for n = 1..5196

Formula

a(n) = A053645(A362009(n) + 1).

Example

The sequence begins:
   n    a(n)     A362240 row
  ---   ----     -----------
    1     0      0;
    2     1      1;
    3     0      0, 0;
    4     3      1, 1;
    5     0      0, 0, 0;
    6     5      1, 0, 1;
    7     7      1, 1, 1;
    8     0      0, 0, 0, 0;
    9    10      1, 0, 1, 0;
   10    13      1, 1, 0, 1;
   11     0      0, 0, 0, 0, 0;
   12     3      0, 0, 0, 1, 1;
   13     4      0, 0, 1, 0, 0;

Mathematica

V = {0}; K = {0}; B = {0}; While[Length@B < 68, y = 0; While[y == 0, i = Length@V; V[[i]]++; While[V[[i]] == 2 && i > 1 , V[[i]] = 0; i--; V[[i]]++]; If[V[[1]] == 2, V = ConstantArray[0, Length@V + 1]]; z = 0; For[a = 1, a <= Length@K - Length@V + 1, a++, If[K[[a ;; a + Length@V - 1]] == V, z = 1; Break[]]]; If[z == 0, AppendTo[K, V]; b = 0; For[c = Length@V, c > 0, c--, b += V[[c]]*2^(Length@V - c)]; AppendTo[B, b]; K = Flatten[K]; y = 1]]]; Print[B]

Prog

(MATLAB) See Links section.
(Python)
from itertools import count, islice, product
def bins(): yield from ("".join(b) for d in count(1) for b in product("01", repeat=d))
def agen(s=""): yield from (int(t, 2) for t in bins() if t not in s and (s:=s+t))
print(list(islice(agen(), 68))) # Michael S. Branicky, Apr 12 2023

Crossrefs

Cf. A362240, A053645, A362009, A118248.

Sequence in context: A249859 A213724 A350082 * A019915 A052123 A285471

Adjacent sequences: A362238 A362239 A362240 * A362242 A362243 A362244

Keyword

nonn,base

Author

Samuel Harkness, Apr 12 2023

Status

approved