cp's OEIS Frontend

A345114 Numbers whose trajectories under the map x -> A345111(x) do not reach a palindrome (conjectured).

%I A345114 #7 Jun 09 2021 23:24:18
%S A345114 49,58,59,67,68,69,76,77,78,79,85,86,87,88,94,95,96,97,103,114,115,
%T A345114 116,117,119,121,124,125,126,128,129,131,134,135,137,138,139,141,142,
%U A345114 143,146,148,149,151,153,154,155,157,158,159,160,161,162,163,164,165,168
%N A345114 Numbers whose trajectories under the map x -> A345111(x) do not reach a palindrome (conjectured).
%C A345114 The trajectories of the given terms do not reach a palindrome in 10000 (10^4) or fewer steps. The trajectory of 49 does not reach a palindrome in 100000 (10^5) or fewer steps.
%o A345114 (PARI) eva(n) = subst(Pol(n), x, 10)
%o A345114 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 A345114 a345112(n, bound) = my(x=n, i=0); while(1, x=x+eva(rot(digits(x))); i++; if(digits(x)==Vecrev(digits(x)), break); if(i > bound, return(-1))); i
%o A345114 is(n) = a345112(n, 10000)==-1
%o A345114 (Python)
%o A345114 def pal(s): return s == s[::-1]
%o A345114 def rotl(s): return s[1:] + s[0]
%o A345114 def A345111(n): return n + int(rotl(str(n)))
%o A345114 def A345112_bd(n, bd=10000):
%o A345114     i, iter, seen = 0, n, set()
%o A345114     while not (iter > n and pal(str(iter))) and iter not in seen and i < bd:
%o A345114         seen.add(iter)
%o A345114         i, iter = i+1, A345111(iter)
%o A345114     return i if iter > n and pal(str(iter)) else 0
%o A345114 def aupto(lim, bd=10000):
%o A345114     return [n for n in range(1, lim+1) if A345112_bd(n, bd=bd) == 0]
%o A345114 print(aupto(168, bd=100)) # _Michael S. Branicky_, Jun 09 2021
%Y A345114 Cf. A023108 (analog for the map x -> A056964(x)), A345110, A345111, A345112, A345113, A345115.
%K A345114 nonn,base
%O A345114 1,1
%A A345114 _Felix Fröhlich_, Jun 09 2021