A352576 -id:A352576 - cp's OEIS frontend

A352575 A109812(n) in binary.

1, 10, 100, 11, 1000, 101, 1010, 10000, 110, 1001, 10010, 1100, 10001, 1110, 100000, 111, 11000, 100001, 10100, 1011, 100100, 10011, 101000, 10101, 100010, 1101, 110000, 1111, 1000000, 10110, 101001, 1000010, 11001, 100110, 1000001, 11010, 100101, 1001000, 10111, 1100000, 11011, 1000100, 100011, 11100, 1000011, 101100, 1010000, 100111, 1011000, 10000000

Offset: 1

N. J. A. Sloane, Apr 04 2022

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..16384
Michael De Vlieger, Bitmap of a(n), n = 1..2^14, horizontally exaggerating each row by 256X.
N. J. A. Sloane, Right-justified table of n, a(n) for n = 1..20000 [Note this is not a b-file.]
N. J. A. Sloane, Right-justified table of n, a(n) for n = 1..10^6 [gzipped file, copied from A352575] [This file was corrupted, but today I replaced it with a corrected version. - _N. J. A. Sloane_, Apr 11 2022]

Cf. A109812, A352576, A352884.

nn = 50, c[] = 0; a[1] = c[1] = 1; u = 2; Do[If[a[i - 1] == u, While[c[u] > 0, u++]]; k = u; While[Nand[c[k] == 0, BitAnd[a[i - 1], k] == 0], k++]; Set[{a[i], c[k]}, {k, i}], {i, Length[s] + 1, nn}]; Array[FromDigits@ IntegerDigits[a[#], 2] &, nn] (* _Michael De Vlieger, Apr 05 2022 *)

A352884 Binary weight of A109812(n).

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 3, 1, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 4, 1, 3, 3, 2, 3, 3, 2, 3, 3, 2, 4, 2, 4, 2, 3, 3, 3, 3, 2, 4, 3, 1, 4, 3, 2, 4, 3, 2, 4, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 2, 4, 3, 3, 4, 2, 5, 2, 4, 2, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 5, 1, 5, 3

Offset: 1

Antti Karttunen, Apr 07 2022

Equivalently, binary weight of A352575.

Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for sequences related to binary expansion of n

Cf. A000120, A109812, A351963, A351964, A351965, A352889.

Cf. also A253589, A352791, A352574, A352575, A352576.

v109812 = readvec("b109812_to10e5.txt"); \\ Prepared from b-file data with gawk ' { print $2 } '
up_to = #v109812;
A109812(n) = v109812[n];
A352884(n) = hammingweight(A109812(n));

a(n) = A000120(A109812(n)) = A000120(A351965(n)).

A352999 a(n) is the least k > 0 such that A109812(n) and A109812(n + 2*k) have different binary lengths.

Original entry on oeis.org

1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 3, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 8

Offset: 1

Rémy Sigrist, Apr 14 2022

			For n = 21:
- we have:
      k  bin(A109812(21+2*k))
      -  --------------------
      0                100100
      1                101000
      2                100010
      3                110000
      4               1000000
- so a(21) = 4.

Rémy Sigrist, Scatterplot of the first million terms
Rémy Sigrist, C++ program

Cf. A109812, A352576, A352998.

a(n) <= A352998(n).

cp's OEIS Frontend

A352575 A109812(n) in binary.

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A352884 Binary weight of A109812(n).

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A352999 a(n) is the least k > 0 such that A109812(n) and A109812(n + 2*k) have different binary lengths.

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