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

49, 58, 59, 67, 68, 69, 76, 77, 78, 79, 85, 86, 87, 88, 94, 95, 96, 97, 103, 114, 115, 116, 117, 119, 121, 124, 125, 126, 128, 129, 131, 134, 135, 137, 138, 139, 141, 142, 143, 146, 148, 149, 151, 153, 154, 155, 157, 158, 159, 160, 161, 162, 163, 164, 165, 168

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..56.

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
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
is(n) = a345112(n, 10000)==-1
(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 A345112_bd(n, bd=10000):
    i, iter, seen = 0, n, set()
    while not (iter > n and pal(str(iter))) and iter not in seen and i < bd:
        seen.add(iter)
        i, iter = i+1, A345111(iter)
    return i if iter > n and pal(str(iter)) else 0
def aupto(lim, bd=10000):
    return [n for n in range(1, lim+1) if A345112_bd(n, bd=bd) == 0]
print(aupto(168, bd=100)) # Michael S. Branicky, Jun 09 2021

Crossrefs

Cf. A023108 (analog for the map x -> A056964(x)), A345110, A345111, A345112, A345113, A345115.

Sequence in context: A044863 A162527 A028915 * A090063 A143164 A304950

Adjacent sequences: A345111 A345112 A345113 * A345115 A345116 A345117

Keyword

nonn,base

Author

Felix Fröhlich, Jun 09 2021

Status

approved