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A337789 Numbers k such that trajectory of k under repeated calculation of fecundity (x -> A070562(x))  eventually reaches 0. 1
0, 1, 5, 10, 15, 18, 20, 21, 22, 24, 27, 30, 35, 40, 42, 44, 46, 48, 50, 51, 55, 59, 60, 63, 64, 66, 67, 69, 70, 74, 75, 77, 80, 83, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 115, 118, 120, 121, 122, 124, 127 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

5 is a term in the sequence because the fecundity of 5 is 1, the fecundity of 1 is 10 and the fecundity of 10 is 0.

7 is not a term in the sequence because the fecundity of 7 is 7 and therefore the fecundity will never become 0.

MAPLE

fec:= proc(n) local k, x, t;

  x:= n;

  for k from 0 do

    t:= convert(convert(x, base, 10), `*`);

    if t = 0 then return k fi;

    x:= x+t

  od

end proc:

filter:= proc(n) local v; option remember;

    v:= fec(n);

    if v = 0 then true

    elif v = n then false

    else procname(v)

    fi

end proc:

select(filter, [$0..1000]); # Robert Israel, Apr 12 2021

MATHEMATICA

fec[n_] := Length @ FixedPointList[# + Times @@ IntegerDigits[#] &, n] - 2; Select[Range[0, 100], FixedPoint[fec, #] == 0 &] (* Amiram Eldar, Sep 22 2020 *)

PROG

(Python)

from math import prod

from functools import lru_cache

def pd(n): return prod(map(int, str(n)))

def A070562(n):

  s = 0

  while pd(n) != 0: n, s = n + pd(n), s + 1

  return s

@lru_cache(maxsize=None)

def ok(n):

  fn = A070562(n)

  if fn == 0: return True

  if fn == n: return False

  return ok(fn)

print(list(filter(ok, range(128)))) # Michael S. Branicky, Apr 12 2021

CROSSREFS

Cf. A070562, A070061, A070257.

Sequence in context: A313672 A313673 A313674 * A282145 A313675 A313676

Adjacent sequences:  A337786 A337787 A337788 * A337790 A337791 A337792

KEYWORD

nonn,easy,base

AUTHOR

Robert Bilinski, Sep 21 2020

EXTENSIONS

More terms from Amiram Eldar, Sep 22 2020

Offset changed by Robert Israel, Apr 12 2021

STATUS

approved

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Last modified September 29 17:18 EDT 2022. Contains 357090 sequences. (Running on oeis4.)