A182273 Starting with 1, smallest integer not having a zero and not yet in the sequence such that two neighboring digits of the sequence multiply to a composite.

1, 4, 2, 3, 5, 6, 7, 8, 9, 14, 16, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84

Offset: 1

Author

Jim Nastos and Eric Angelini, Apr 22 2012

Keywords

• nonn
• base
• easy
• nice

Comments

The number after 1 has to be 4, because the product 1*4 must be composite.

Then 2 is OK, because 4*2 = 8 is composite.

Then 3, because 2*3 = 6 is composite, and so on.

Note that 14 is the term after 9 because 10 is now the smallest candidate, but 10 has a 0 digit, 11 consists of two unit digits, and 12 and 13 have digit products 2 and 3, which are prime. - T. D. Noe, Apr 25 2012

Links

• Dominic McCarty, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A182272.

Programs

Python

a, z = [1], [1,2,3,5,7]
while len(a) < 100:
    k, s = 2, "2"
    while (k in a) or ("0" in s) or (a[-1] % 10 * int(s[0]) in z) or \
        any(int(s[n]) * int(s[n+1]) in z for n in range(0, len(s)-1)): s, k = str(k+1), k+1
    a.append(k)
print(a) # Dominic McCarty, Jan 30 2025