A366912 -id:A366912 - cp's OEIS frontend

A366913 a(n) is the least k such that A366912(k) = n.

1, 2, 3, 4, 9, 10, 23, 28, 29, 84, 170, 353, 805, 850, 2171, 4860, 11815, 28025, 31539, 131252, 318231, 406904, 1612758, 2461032, 9917597, 11551434, 36824781, 80492173, 206009383, 505512671, 1361256869, 2467754261

Offset: 0

Rémy Sigrist, Oct 27 2023

a(n) corresponds to the index of the first term of A364054 with height n.

Rémy Sigrist, PARI program
Rémy Sigrist, C++ program

Cf. A064290, A364054, A366912.

See Links section.
(C++) See Links section.

from itertools import count
from sympy import nextprime
def A366913(n):
    a, aset, p, c = 1, {0,1}, 2, 0
    for i in count(1):
        if c == n:
            return i
        k, b = divmod(a,p)
        for j in count(-k):
            if b not in aset:
                aset.add(b)
                a, p = b, nextprime(p)
                c += j
                break
            b += p # Chai Wah Wu, Oct 27 2023

a(29) from Chai Wah Wu, Oct 27 2023

a(30)-a(31) from Chai Wah Wu, Oct 28 2023

A366911 a(n) = (A364054(n+1) - A364054(n)) / prime(n) (where prime(n) denotes the n-th prime number).

Original entry on oeis.org

1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -3, 2, -2, 1, -1, 1, -1, 2, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1

Offset: 1

Rémy Sigrist, Oct 27 2023

sign

a(n) is the number of steps of size prime(n) in going from A364054(n) to A364054(n+1).

			a(7) = (A364054(8) - A364054(7)) / prime(7) = (19 - 2) / 17 = 1.

N. J. A. Sloane, Table of n, a(n) for n = 1..9999
Rémy Sigrist, PARI program

Cf. A160357, A364054, A366912 (partial sums).

nn = 2^16; c[] := False; m[] := 0; j = 1; c[0] = c[1] = True;
  Monitor[Do[p = Prime[n - 1]; r = Mod[j, p];
    While[Set[k, p m[p] + r ]; c[k], m[p]++];
    Set[{a[n - 1], c[k], j}, {(k - j)/p, True, k}], {n, 2, nn + 1}], n];
Array[a, nn] (* Michael De Vlieger, Oct 27 2023 *)

PARI
```
See Links section.
```

from itertools import count, islice
from sympy import nextprime
def A366911_gen(): # generator of terms
    a, aset, p = 1, {0,1}, 2
    while True:
        k, b = divmod(a,p)
        for i in count(-k):
            if b not in aset:
                aset.add(b)
                a, p = b, nextprime(p)
                yield i
                break
            b += p
A366911_list = list(islice(A366911_gen(),30)) # Chai Wah Wu, Oct 27 2023

cp's OEIS Frontend

A366913 a(n) is the least k such that A366912(k) = n.

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