A331835 -id:A331835 - cp's OEIS frontend

A345297 a(n) is the least k >= 0 such that A331835(k) = n.

0, 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 22, 23, 26, 27, 29, 30, 31, 43, 45, 46, 47, 54, 55, 58, 59, 61, 62, 63, 94, 95, 107, 109, 110, 111, 118, 119, 122, 123, 125, 126, 127, 187, 189, 190, 191, 222, 223, 235, 237, 238, 239, 246, 247, 250, 251, 253, 254, 255

Offset: 0

Rémy Sigrist, Jun 13 2021

Sequence A200947 gives the position of the last occurrence of a number in A331835.

			We have:
           n|  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18
  ----------+------------------------------------------------------------------
  A331835(n)|  0  1  2  3  3  4  5  6  5  6   7   8   8   9  10  11   7   8   9
So a(0) = 0,
   a(1) = 1,
   a(2) = 2,
   a(3) = 3,
   a(4) = 5,
   a(5) = 6,
   a(6) = 7,
   a(7) = 10,
   a(8) = 11,
   a(9) = 13,
   a(10) = 14,
   a(11) = 15.

Rémy Sigrist, Table of n, a(n) for n = 0..2000
Rémy Sigrist, C program for A345297

Cf. A014284, A200947, A331835.

C
```
See Links section.
```

from sympy import prime
def p(n): return prime(n) if n >= 1 else 1
def A331835(n): return sum(p(i)*int(b) for i, b in enumerate(bin(n)[:1:-1]))
def adict(klimit):
    adict = dict()
    for k in range(klimit+1):
        fk = A331835(k)
        if fk not in adict: adict[fk] = k
    n, alst = 0, []
    while n in adict: alst.append(adict[n]); n += 1
    return alst
print(adict(255)) # Michael S. Branicky, Jun 13 2021

a(A014284(n)) = 2^n - 1.

a(n) <= A200947(n).

A368577 Irregular table T(n, k), n >= 0, k = 1..A036497(n), read by rows; the n-th row lists the numbers m such that A331835(m) = n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 16, 11, 12, 17, 13, 18, 14, 19, 20, 15, 21, 32, 22, 24, 33, 23, 25, 34, 64, 26, 35, 36, 65, 27, 28, 37, 66, 29, 38, 40, 67, 68, 30, 39, 41, 69, 128, 31, 42, 48, 70, 72, 129, 43, 44, 49, 71, 73, 130, 256, 45, 50, 74, 80, 131, 132, 257

Offset: 0

Rémy Sigrist, Dec 31 2023

As a flat sequence, this is a permutation of the nonnegative integers (with inverse A368578).

			Table T(n, k) begins:
  n   n-th row
  --  ------------------
   0  0
   1  1
   2  2
   3  3, 4
   4  5
   5  6, 8
   6  7, 9
   7  10, 16
   8  11, 12, 17
   9  13, 18
  10  14, 19, 20
  11  15, 21, 32
  12  22, 24, 33
  13  23, 25, 34, 64
  14  26, 35, 36, 65
  15  27, 28, 37, 66
  16  29, 38, 40, 67, 68

Rémy Sigrist, Table of n, a(n) for n = 0..10888 (rows for n = 0..104 flattened)
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A036497, A200947, A331835, A345101, A345297, A368578 (inverse).

PARI
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\\ See Links section.
```

T(n, 1) = A345297(n).

T(n, A036497(n)) = A200947(n).

cp's OEIS Frontend

A345297 a(n) is the least k >= 0 such that A331835(k) = n.

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