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

Author

Eric Angelini and Carole Dubois, Aug 21 2021

Keywords

• base
• nonn

Examples

			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.
		

Crossrefs

Cf. A333774, A347181.

Programs

Python

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