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

Author

Samuel Harkness, Apr 12 2023

Keywords

• nonn
• base

Examples

			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;
		

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

Crossrefs

Cf. A362240, A053645, A362009, A118248.

Programs

MATLAB

See Links section.

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]

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

Formula

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