A353727 -id:A353727 - cp's OEIS frontend

A353715 a(n) = b(n)+b(n+1), where b is A353709.

1, 3, 6, 12, 11, 19, 28, 44, 49, 23, 46, 104, 69, 15, 58, 113, 79, 142, 161, 51, 86, 77, 43, 54, 92, 107, 167, 156, 90, 102, 61, 155, 226, 109, 157, 242, 354, 277, 63, 234, 449, 279, 126, 233, 387, 286, 125, 481, 410, 63, 357, 456, 143, 87, 240, 171, 95, 372, 419, 207, 348, 433, 231, 334, 313, 183, 462, 840, 531, 63, 492, 961, 543, 254, 992, 783, 127

Offset: 0

N. J. A. Sloane, May 09 2022

Created in an attempt to show that every number appears in A353709. For example, if one could show that the present sequence had a subsequence which was divisible by ever-increasing powers of 2, the desired result would follow. See A353724, A353725, A353726, A353727 for more about this topic.

N. J. A. Sloane, Table of n, a(n) for n = 0..16383
Walter Trump, Log-log plot of first 2^24 terms. Green dots (which overwrite the black dots) indicate terms a(n) which are divisible by 64.

Cf. A353709, A353724, A353725, A353726, A353727.

g:= proc() false end: t:= 2:
b:= proc(n) option remember; global t; local k; if n<2 then n
      else for k from t while g(k) or Bits[And](k, b(n-2))>0
      or Bits[And](k, b(n-1))>0 do od; g(k):=true;
      while g(t) do t:=t+1 od; k fi
    end:
a:= n-> b(n)+b(n+1):
seq(a(n), n=0..100);  # Alois P. Heinz, May 09 2022

g[_] = False ; t = 2;
b[n_] := b[n] = Module[{k}, If[n < 2, n,
   For[k = t, g[k] || BitAnd[k, b[n-2]] > 0 ||
   BitAnd[k, b[n-1]] > 0, k++]; g[k] = True;
   While[g[t], t = t+1]; k]];
a[n_] := b[n] + b[n+1];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jul 07 2022, after Alois P. Heinz *)

from itertools import count, islice
def A353715_gen(): # generator of terms
    s, a, b, c, ab = {0,1}, 0, 1, 2, 1
    yield 1
    while True:
        for n in count(c):
            if not (n & ab or n in s):
                yield b+n
                a, b = b, n
                ab = a|b
                s.add(n)
                while c in s:
                    c += 1
                break
A353715_list = list(islice(A353715_gen(),30)) # Chai Wah Wu, May 11 2022

A353725 Records in A353724.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 12, 13, 16, 17, 18

Offset: 1

N. J. A. Sloane, May 11 2022

Motivated by a comment in A353715.

			Table from _Walter Trump_, May 11 2022, showing initial terms of A353725 (column 1) and A353726 (column 3). The central column shows the corresponding entry of A353715 written in base 2.
   0                                1         0
   1                              110         2
   2                             1100         3
   3                          1101000        11
   4                         11110000        54
   5                       1111100000        74
   6                      11101000000        88
   7                     110110000000       183
  12                11111000000000000      3913
  13          10011111110000000000000    124845
  16      111111111110000000000000000   2469947
  17     1111111101100000000000000000   4005550
  18  1011111111111000000000000000000  19917707

Cf. A353709, A353715, A353724, A353726, A353727.

a(10)-a(13) from Walter Trump, May 11 2022

cp's OEIS Frontend

A353715 a(n) = b(n)+b(n+1), where b is A353709.

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A353725 Records in A353724.

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A353726 Indices of records in A353724.

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