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

1,1

Comments

First differs from A061563 at n = 19.

Links

Table of n, a(n) for n=1..48.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A068062 A088169 A061563 * A099994 A068065 A278228

Adjacent sequences: A345110 A345111 A345112 * A345114 A345115 A345116

Keyword

nonn,base,more

Author

Felix Fröhlich, Jun 09 2021

Status

approved