A341694 -id:A341694 - cp's OEIS frontend

A341699 a(n) is the least m such that A341694(m, k) = n for some k > 0.

1, 2, 2, 4, 2, 11, 4, 2, 5, 12, 4, 9, 2, 8, 17, 12, 5, 4, 24, 32, 2, 48, 8, 13, 10, 12, 19, 16, 4, 25, 5, 18, 21, 2, 33, 36, 8, 11, 34, 45, 37, 9, 68, 13, 16, 66, 4, 77, 10, 24, 27, 47, 17, 153, 2, 39, 5, 48, 95, 8, 22, 51, 18, 26, 21, 49, 71, 12, 44, 11, 36

Offset: 1

Rémy Sigrist, Feb 17 2021

			The first row of A341694 contains only 1's:
- so a(1) = 1.
The second row of A341694 contains the positive Fibonacci numbers:
- so a(2) = a(3) = a(5) = a(8) = a(13) = a(21) = a(34) = a(55) = ..., = 2.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Logarithmic scatterplot of the first 2^18 terms
Rémy Sigrist, PARI program for A341699

Cf. A070939, A341285, A341694.

PARI
```
See Links section.
```

a(n) <= 2^(n-1).

A341285(n) = A070939(a(n)).

A341746 If the runs in the binary expansion of n are (r_1, ..., r_k), then the runs in the binary expansion of a(n) are (r_1 + ... + r_k, r_1, ..., r_{k-1}).

Original entry on oeis.org

1, 6, 3, 14, 29, 28, 7, 30, 123, 122, 61, 60, 121, 120, 15, 62, 503, 502, 251, 250, 501, 500, 125, 124, 499, 498, 249, 248, 497, 496, 31, 126, 2031, 2030, 1015, 1014, 2029, 2028, 507, 506, 2027, 2026, 1013, 1012, 2025, 2024, 253, 252, 2023, 2022, 1011, 1010

Offset: 1

Rémy Sigrist, Feb 18 2021

This sequence is related to A341694 (see Formula section).
All terms are distinct.
If a(n) > n, then a(n) does not appear in A341699.

			The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   1     1       1          1
   2     6      10        110
   3     3      11         11
   4    14     100       1110
   5    29     101      11101
   6    28     110      11100
   7     7     111        111
   8    30    1000      11110
   9   123    1001    1111011
  10   122    1010    1111010
  11    61    1011     111101
  12    60    1100     111100
  13   121    1101    1111001
  14   120    1110    1111000
  15    15    1111       1111

Rémy Sigrist, Table of n, a(n) for n = 1..8192
Rémy Sigrist, Binary plot of the first 255 terms
Index entries for sequences related to binary expansion of n

Cf. A005811, A070939, A090996, A126646, A341694, A341699.

toruns(n) = { my (r=[]); while (n, my (v=valuation(n+n%2, 2)); n\=2^v; r=concat(v, r)); r }
fromruns(r) = { my (v=0); for (k=1, #r, v=(v+k%2)*2^r[k]-k%2); v }
a(n) = { my (r=toruns(n)); fromruns(concat(vecsum(r), r[1..#r-1])) }

A341694(a(n), k) = A341694(n, k+1).
a(n) = n iff n belongs to A126646.
A090996(a(n)) = A070939(n).
A090996(a(n)) > A070939(a(n)) / 2.
A005811(a(n)) = A005811(n).

cp's OEIS Frontend

A341699 a(n) is the least m such that A341694(m, k) = n for some k > 0.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula