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A357826
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Base-10 weaker Skolem-Langford numbers.
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4
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231213, 312132, 12132003, 23121300, 23421314, 30023121, 31213200, 41312432, 1214230043, 1312432004, 2342131400, 2412134003, 3004312142, 3400324121, 4002342131, 4131243200, 4562342536, 4635243265, 5364235246, 5623425364, 6352432654, 6425324635, 14156742352637, 14167345236275
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(Python)
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)
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CROSSREFS
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KEYWORD
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nonn,base,easy,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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