A370952 -id:A370952 - cp's OEIS frontend

A370975 a(n) = (A370952(n+1) - A370952(n)) /(2*n+1).

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

Offset: 1

N. J. A. Sloane, Apr 17 2024

sign

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A370952, A372052.

from itertools import count, islice
def A370975_gen(): # generator of terms
    a, aset = 1, {0,1}
    for p in count(3,2):
        for b in count(a%p,p):
            if b not in aset:
                aset.add(b)
                yield (b-a)//p
                a = b
                break
A370095_list = list(islice(A370975_gen(),20)) # Chai Wah Wu, Apr 17 2024

A372052 Where n appears in A370952, or -1 if n never appears there.

Original entry on oeis.org

1, 4, 49, 2, 8, 24, 47, 22, 3, 20, 5, 18, 44, 16, 175, 14, 42, 12, 173, 10, 40, 6, 171, 88, 38, 335, 169, 86, 36, 333, 167, 84, 34, 331, 7, 82, 32, 329, 9, 80, 11, 327, 13, 78, 15, 325, 17, 76, 19, 323, 21, 74, 23, 321, 25, 72, 160, 319, 7468, 70, 158, 317, 25099

Offset: 1

N. J. A. Sloane, Apr 17 2024

nonn

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A370952, A370975.

from itertools import count
def A372052(n):
    a, aset = 1, {0,1}
    for p in count(3,2):
        if a == n:
            return p>>1
        for b in count(a%p,p):
            if b not in aset:
                aset.add(b)
                a = b
                break # Chai Wah Wu, Apr 17 2024

# faster for initial segment of sequence
def A372052_gen(): # uses A370952_gen/imports from Chai Wah Wu in A370952
    adict, n = dict(), 1
    for i, v in enumerate(A370952_gen(), 1):
        if v >= n and v not in adict:
            adict[v] = i
            while n in adict:
                yield adict[n]; del adict[n]; n += 1
print(list(islice(A372052_gen(), 63))) # Michael S. Branicky, Apr 18 2024

More terms from Chai Wah Wu, Apr 17 2024

cp's OEIS Frontend

A370975 a(n) = (A370952(n+1) - A370952(n)) /(2*n+1).

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A372052 Where n appears in A370952, or -1 if n never appears there.

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