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A357826 Base-10 weaker Skolem-Langford numbers.

%I A357826 #46 Dec 11 2022 13:51:41
%S A357826 231213,312132,12132003,23121300,23421314,30023121,31213200,41312432,
%T A357826 1214230043,1312432004,2342131400,2412134003,3004312142,3400324121,
%U A357826 4002342131,4131243200,4562342536,4635243265,5364235246,5623425364,6352432654,6425324635,14156742352637,14167345236275
%N A357826 Base-10 weaker Skolem-Langford numbers.
%C A357826 Self-describing numbers: between two digits "d" there are d digits.
%C A357826 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).
%C A357826 "weaker" means that when the smallest digit is x, all digits from x to the largest digit must be present.
%C A357826 The smallest digit x could be any value, but it turns out the biggest is x = 3 with 28 terms in total.
%C A357826 This sequence has 3390 terms. The largest term is 867315136875420024.
%C A357826 See A108116 for the "weak" variant with another constraint, and A132291 for the "strong" variant with more constraints.
%H A357826 Michael S. Branicky, <a href="/A357826/b357826.txt">Table of n, a(n) for n = 1..3390</a>
%e A357826 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.
%o A357826 (Python)
%o A357826 def afull(): # SL() is in A108116
%o A357826     alst = []
%o A357826     for d in range(1, 11):
%o A357826         for b in range(11-d):
%o A357826             dset = ("0123456789")[b:b+d]
%o A357826             s = [0 for _ in range(2*d)]
%o A357826             for an in sorted(SL(dset, s)):
%o A357826                 alst.append(an)
%o A357826     return sorted(alst)
%o A357826 print(afull()[:22]) # _Michael S. Branicky_, Oct 14 2022
%Y A357826 Cf. base-10 Skolem-Langford numbers: A108116 (weak), A132291 (strong), A339803 (super weak).
%K A357826 nonn,base,easy,fini,full
%O A357826 1,1
%A A357826 _Marc Morgenegg_, Oct 14 2022
%E A357826 More terms from _David A. Corneth_, Oct 14 2022