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A387242 a(n) is the least k such that A334676(k) != k and the decimal string of n appears in A334676(k).

%I A387242 #10 Aug 27 2025 21:59:22
%S A387242 2,42,26,28,102,32,85,172,95,20,22,242,26,28,302,32,85,236,95,402,42,
%T A387242 442,115,482,502,522,162,562,145,260,62,1615,266,268,712,272,148,772,
%U A387242 278,802,82,842,215,882,902,92,235,962,245,1002,102,1042,265,1078,1102,112,285,1162
%N A387242 a(n) is the least k such that A334676(k) != k and the decimal string of n appears in A334676(k).
%e A387242 A334676(242) = 121, the first term whose decimal expansion contains the substring "12"; hence a(12) = 242.
%e A387242 A334676(21) = A334676(42) = 21 contains "2" but a(2) = 42 since the first does not satisfy A334676(k) != k.
%o A387242 (Python) # uses A334676() and neighs() from A334676
%o A387242 from itertools import count, islice
%o A387242 def subs(s): yield from (s[i:j] for i in range(len(s)) for j in range(i+1, len(s)+1))
%o A387242 def agen(): # generator of terms
%o A387242     adict, n = dict(), 1
%o A387242     for k in count(1):
%o A387242         v = A334676(k)
%o A387242         if v != k:
%o A387242             for t in subs(str(v)):
%o A387242                 if (ti:=int(t)) not in adict:
%o A387242                     adict[ti] = k
%o A387242                     while n in adict:
%o A387242                         yield adict[n]
%o A387242                         n += 1
%o A387242 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Aug 23 2025
%Y A387242 Cf. A334676.
%K A387242 nonn,base,new
%O A387242 1,1
%A A387242 _Ali Sada_, Aug 23 2025