A345113 - OEIS

%I #6 Jun 09 2021 23:22:53

%S 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 77,88,99,323,121,33,44,55,66,77,88,99,323,121,683737386,44,55,66,77,

%U 88,99,323,121,683737386

%N 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 First differs from A061563 at n = 19.

%e For n = 19: 19 + 91 = 110, 110 + 101 = 211, 211 + 112 = 323 and 323 is a palindrome, so a(19) = 323.

%o (PARI) eva(n) = subst(Pol(n), x, 10)

%o 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 a(n) = my(x=n); while(1, x=x+eva(rot(digits(x))); if(digits(x)==Vecrev(digits(x)), return(x)))

%o (Python)

%o def pal(s): return s == s[::-1]

%o def rotl(s): return s[1:] + s[0]

%o def A345111(n): return n + int(rotl(str(n)))

%o def a(n):

%o     i, iter, seen = 0, n, set()

%o     while not (iter > n and pal(str(iter))) and iter not in seen:

%o         seen.add(iter)

%o         i, iter = i+1, A345111(iter)

%o     return iter if iter > n and pal(str(iter)) else 0

%o print([a(n) for n in range(1, 49)]) # _Michael S. Branicky_, Jun 09 2021

%Y Cf. A002113, A061563, A345110, A345111, A345112, A345114, A345115.

%K nonn,base,more

%O 1,1

%A _Felix Fröhlich_, Jun 09 2021