A368382 -id:A368382 - cp's OEIS frontend

A368383 a(n) = index of n in A368382, or -1 if n is missing from that sequence.

1, 7, 2, 5, 13, 3, 67, 35, 11, 33, 4, 31, 6, 29, 8, 27, 63, 25, 327, 23, 61, 21, 325, 19, 59, 17, 323, 15, 57, 9, 321, 175, 55, 173, 15490, 171, 53, 169, 317, 167, 51, 165, 1167, 163, 49, 161, 10, 159, 47, 157, 12, 155, 45, 153, 14, 151, 16, 149, 18, 147, 20, 145, 22, 143, 24, 141, 26, 139, 28, 137, 30, 135, 32, 133, 34

Offset: 1

N. J. A. Sloane, Mar 03 2024

nonn

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

from itertools import count
def A368383(n):
    a, aset, p = 1, {0,1}, 2
    for c in count(1):
        if a==n: return c
        for b in count(a%p,p):
            if b not in aset:
                aset.add(b)
                a, p = b, 3 if p == 2 else p+2
                break # Chai Wah Wu, Mar 05 2024

# faster for initial segment of sequence
def A368383_gen(): # uses A368382_gen/imports from Chai Wah Wu in A368382
    adict, n = dict(), 1
    for i, v in enumerate(A368382_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(A368383_gen(), 63))) # Michael S. Branicky, Apr 18 2024

A370952 a(1) = 1; for n > 1, a(n) is the least positive integer not already in the sequence such that a(n) == a(n-1) (mod 2*n-1).

Original entry on oeis.org

1, 4, 9, 2, 11, 22, 35, 5, 39, 20, 41, 18, 43, 16, 45, 14, 47, 12, 49, 10, 51, 8, 53, 6, 55, 106, 159, 104, 161, 102, 163, 37, 167, 33, 171, 29, 175, 25, 179, 21, 183, 17, 187, 13, 191, 100, 7, 197, 3, 201, 302, 96, 306, 92, 310, 88, 314, 84, 318, 80, 322, 76, 326, 72, 330, 68, 334, 64, 338, 60, 342, 56, 346, 52, 350

Offset: 1

N. J. A. Sloane, Mar 07 2024

nonn

Very similar to A368382, except that there the differences are controlled by the sequence {2,3,5,7,9,11,13,15,...} (A004280), whereas here they are controlled by {3,5,7,9,11,13,15,...}.

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

Cf. A004280, A368382, A370975, A372052 (where n appears).

from itertools import count, islice
def A370952_gen(): # generator of terms
    a, aset = 1, {0,1}
    for p in count(3,2):
        yield a
        for b in count(a%p,p):
            if b not in aset:
                aset.add(b)
                a = b
                break
A370952_list = list(islice(A370952_gen(),20)) # Chai Wah Wu, Apr 17 2024

cp's OEIS Frontend

A368383 a(n) = index of n in A368382, or -1 if n is missing from that sequence.

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A370952 a(1) = 1; for n > 1, a(n) is the least positive integer not already in the sequence such that a(n) == a(n-1) (mod 2*n-1).

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Python