A347181 -id:A347181 - cp's OEIS frontend

A347180 Lexicographically earliest sequence of distinct positive integers such that the first digit of a(n) is visible in a(n) * a(n+1).

1, 10, 11, 12, 9, 21, 2, 6, 16, 7, 25, 5, 3, 13, 8, 23, 4, 26, 17, 30, 31, 14, 15, 34, 39, 24, 18, 45, 32, 41, 28, 19, 22, 33, 40, 35, 38, 36, 37, 29, 42, 20, 46, 27, 47, 52, 49, 50, 43, 48, 51, 54, 64, 44, 55, 53, 65, 56, 63, 58, 61, 60, 66, 57, 62, 59, 67, 68, 69, 72, 76, 75, 73, 79, 82, 71, 70

Offset: 1

Eric Angelini and Carole Dubois, Aug 21 2021

			a(1) * a(2) =  1 * 10 =  10;
a(2) * a(3) = 10 * 11 = 110;
a(3) * a(4) = 11 * 12 = 132;
a(4) * a(5) = 12 *  9 = 108;
a(5) * a(6) =  9 * 21 = 189; etc.

Cf. A333774, A347181.

def aupton(terms):
    alst, aset = [1], {1}
    while len(alst) < terms:
        an, target = 2, str(alst[-1])[0]
        while an in aset or target not in str(alst[-1]*an): an += 1
        alst.append(an); aset.add(an)
    return alst
print(aupton(200)) # Michael S. Branicky, Aug 21 2021

A347182 Lexicographically earliest sequence of distinct positive integers such that all digits of a(n) are visible in a(n) * a(n+1).

Original entry on oeis.org

1, 10, 11, 91, 9, 21, 6, 16, 26, 24, 18, 45, 12, 51, 3, 13, 27, 36, 38, 22, 56, 28, 29, 32, 41, 4, 31, 23, 14, 76, 89, 55, 47, 42, 7, 25, 5, 15, 34, 69, 39, 61, 92, 86, 8, 35, 67, 100, 17, 43, 78, 87, 33, 71, 81, 64, 54, 66, 96, 72, 99, 101, 109, 90, 44, 102, 60, 46, 79, 48, 58, 98, 151, 75, 37, 19

Offset: 1

Eric Angelini and Carole Dubois, Aug 22 2021

a(3) = 11 has two digits "1"; they must both be visible in a(3) * a(4) and this is the case as a(3) * a(4) = 11 * 91 = 1001.

Is this a permutation of the positive integers? - Pontus von Brömssen, Aug 23 2021

			a(1) * a(2) =  1 * 10 =   10;
a(2) * a(3) = 10 * 11 =  110;
a(3) * a(4) = 11 * 91 = 1001;
a(4) * a(5) = 91 *  9 =  819;
a(5) * a(6) =  9 * 21 =  189; etc.

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Cf. A347180, A347181, A347183.

from collections import Counter
def A347182_list(n):
    a = [1]
    m = 2  # Smallest number not yet in a.
    M = 1  # Largest number in a so far.
    used = []  # Indicator for what numbers m..M that are in a so far.
    for i in range(n - 1):
        c0 = Counter(str(a[-1]))
        x = m
        while 1:
            if x > M or not used[x - m]:
                c = Counter(str(a[-1] * x))
                if all(c[d] >= c0[d] for d in "0123456789"):
                    break
            x += 1
        if x > M:
            used.extend([0] * (x - M - 1) + [1])
            M = x
        else:
            used[x - m] = 1
        if x == m:
            j = next((j for j in range(len(used)) if not used[j]), len(used))
            m += j
            del used[:j]
        a.append(x)
    return a  # Pontus von Brömssen, Aug 24 2021

A347183 Lexicographically earliest sequence of distinct positive integers such that all digits of a(n) are visible in a(n) + a(n+1).

Original entry on oeis.org

1, 9, 10, 90, 19, 72, 55, 100, 900, 109, 81, 27, 45, 200, 802, 18, 63, 73, 64, 82, 46, 118, 693, 243, 99, 300, 703, 334, 1000, 9000, 1009, 891, 198, 621, 405, 135, 180, 630, 406, 54, 91, 28, 154, 261, 351, 162, 450, 595, 360, 270, 432, 811, 207, 495, 459, 36, 127, 144, 297, 675, 892, 397, 342

Offset: 1

Eric Angelini and Carole Dubois, Aug 22 2021

a(7) = 55 has two digits "5"; they must both be visible in a(7) + a(8) and this is the case as a(7) + a(8) = 55 + 100 = 155.

			a(1) + a(2) =  1 +  9 =  10;
a(2) + a(3) =  9 + 10 =  19;
a(3) + a(4) = 10 + 90 = 100;
a(4) + a(5) = 90 + 19 = 109;
a(5) + a(6) = 19 + 72 =  91; etc.

Cf. A347180, A347181, A347182.

cp's OEIS Frontend

A347180 Lexicographically earliest sequence of distinct positive integers such that the first digit of a(n) is visible in a(n) * a(n+1).

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A347182 Lexicographically earliest sequence of distinct positive integers such that all digits of a(n) are visible in a(n) * a(n+1).

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Python

A347183 Lexicographically earliest sequence of distinct positive integers such that all digits of a(n) are visible in a(n) + a(n+1).

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