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A345114 Numbers whose trajectories under the map x -> A345111(x) do not reach a palindrome (conjectured). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 2 09:22 EDT 2021. Contains 346422 sequences. (Running on oeis4.)