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A345113 a(n) is the palindrome reached after A345112(n) steps under repeated applications of the map x -> A345111(x), starting with n, or 0 if no palindrome is ever reached.

%I A345113 #6 Jun 09 2021 23:22:53
%S A345113 2,4,6,8,11,33,55,77,99,11,22,33,44,55,66,77,88,99,323,22,33,44,55,66,
%T A345113 77,88,99,323,121,33,44,55,66,77,88,99,323,121,683737386,44,55,66,77,
%U A345113 88,99,323,121,683737386
%N A345113 a(n) is the palindrome reached after A345112(n) steps under repeated applications of the map x -> A345111(x), starting with n, or 0 if no palindrome is ever reached.
%C A345113 First differs from A061563 at n = 19.
%e A345113 For n = 19: 19 + 91 = 110, 110 + 101 = 211, 211 + 112 = 323 and 323 is a palindrome, so a(19) = 323.
%o A345113 (PARI) eva(n) = subst(Pol(n), x, 10)
%o A345113 rot(vec) = if(#vec < 2, return(vec)); my(s=concat(Str(2), ".."), v=[]); s=concat(s, Str(#vec)); v=vecextract(vec, s); v=concat(v, vec[1]); v
%o A345113 a(n) = my(x=n); while(1, x=x+eva(rot(digits(x))); if(digits(x)==Vecrev(digits(x)), return(x)))
%o A345113 (Python)
%o A345113 def pal(s): return s == s[::-1]
%o A345113 def rotl(s): return s[1:] + s[0]
%o A345113 def A345111(n): return n + int(rotl(str(n)))
%o A345113 def a(n):
%o A345113     i, iter, seen = 0, n, set()
%o A345113     while not (iter > n and pal(str(iter))) and iter not in seen:
%o A345113         seen.add(iter)
%o A345113         i, iter = i+1, A345111(iter)
%o A345113     return iter if iter > n and pal(str(iter)) else 0
%o A345113 print([a(n) for n in range(1, 49)]) # _Michael S. Branicky_, Jun 09 2021
%Y A345113 Cf. A002113, A061563, A345110, A345111, A345112, A345114, A345115.
%K A345113 nonn,base,more
%O A345113 1,1
%A A345113 _Felix Fröhlich_, Jun 09 2021