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A357826
Base-10 weaker Skolem-Langford numbers.
4
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
1,1
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.
LINKS
EXAMPLE
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.
PROG
(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
CROSSREFS
Cf. base-10 Skolem-Langford numbers: A108116 (weak), A132291 (strong), A339803 (super weak).
Sequence in context: A015319 A270515 A179624 * A050998 A237462 A244349
KEYWORD
nonn,base,easy,fini,full
AUTHOR
Marc Morgenegg, Oct 14 2022
EXTENSIONS
More terms from David A. Corneth, Oct 14 2022
STATUS
approved