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.

2, 4, 6, 8, 11, 33, 55, 77, 99, 11, 22, 33, 44, 55, 66, 77, 88, 99, 323, 22, 33, 44, 55, 66, 77, 88, 99, 323, 121, 33, 44, 55, 66, 77, 88, 99, 323, 121, 683737386, 44, 55, 66, 77, 88, 99, 323, 121, 683737386

Offset: 1

Author

Felix Fröhlich, Jun 09 2021

Keywords

• nonn
• base
• more

Comments

First differs from A061563 at n = 19.

Examples

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

Crossrefs

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

Programs

PARI

eva(n) = subst(Pol(n), x, 10)
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
a(n) = my(x=n); while(1, x=x+eva(rot(digits(x))); if(digits(x)==Vecrev(digits(x)), return(x)))

Python

def pal(s): return s == s[::-1]
def rotl(s): return s[1:] + s[0]
def A345111(n): return n + int(rotl(str(n)))
def a(n):
    i, iter, seen = 0, n, set()
    while not (iter > n and pal(str(iter))) and iter not in seen:
        seen.add(iter)
        i, iter = i+1, A345111(iter)
    return iter if iter > n and pal(str(iter)) else 0
print([a(n) for n in range(1, 49)]) # Michael S. Branicky, Jun 09 2021