A357826 Base-10 weaker Skolem-Langford numbers.

231213, 312132, 12132003, 23121300, 23421314, 30023121, 31213200, 41312432, 1214230043, 1312432004, 2342131400, 2412134003, 3004312142, 3400324121, 4002342131, 4131243200, 4562342536, 4635243265, 5364235246, 5623425364, 6352432654, 6425324635, 14156742352637, 14167345236275

Offset: 1

Author

Marc Morgenegg, Oct 14 2022

Keywords

• nonn
• base
• easy
• fini
• full

Comments

Self-describing numbers: between two digits "d" there are d digits.

a(n) has either 0 or 2 instances of any digit, hence even number of digits, and in fact the number of digits of a(n) == 0 or 2 or 6 (mod 8).

"weaker" means that when the smallest digit is x, all digits from x to the largest digit must be present.

The smallest digit x could be any value, but it turns out the biggest is x = 3 with 28 terms in total.

This sequence has 3390 terms. The largest term is 867315136875420024.

See A108116 for the "weak" variant with another constraint, and A132291 for the "strong" variant with more constraints.

Examples

			41312432 is a term since both 4's are separated by four digits, the 1's by one, the 3's by three, the 2's by two. Every digit from 1 to 4 is present.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..3390

Crossrefs

Cf. base-10 Skolem-Langford numbers: A108116 (weak), A132291 (strong), A339803 (super weak).

Programs

Python

def afull(): # SL() is in A108116
    alst = []
    for d in range(1, 11):
        for b in range(11-d):
            dset = ("0123456789")[b:b+d]
            s = [0 for _ in range(2*d)]
            for an in sorted(SL(dset, s)):
                alst.append(an)
    return sorted(alst)
print(afull()[:22]) # Michael S. Branicky, Oct 14 2022

Extensions

More terms from David A. Corneth, Oct 14 2022