The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A352595

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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Positive integers that are fixed points for the map x->f^k(x) for some k>1, where f(x) is the product of squares of nonzero digits of x.
(history; published version)

#8 by N. J. A. Sloane at Sat Mar 26 14:50:11 EDT 2022

STATUS

proposed

approved

#7 by Michael S. Branicky at Thu Mar 24 19:49:04 EDT 2022

STATUS

editing

proposed

#6 by Michael S. Branicky at Thu Mar 24 19:48:37 EDT 2022

PROG

print(list(islice(agen(), 11))) # _Michael S. Branicky_, Mar 24 2022

STATUS

proposed

editing

Discussion

Thu Mar 24

19:48

Michael S. Branicky: done.  thank you.

#5 by Michael S. Branicky at Thu Mar 24 15:49:36 EDT 2022

STATUS

editing

proposed

Discussion

Thu Mar 24

17:53

Michel Marcus: I would move your A351327 comment here

17:53

Michel Marcus: No need to sign python program

#4 by Michael S. Branicky at Thu Mar 24 14:11:06 EDT 2022

KEYWORD

nonn,base,more,changed

#3 by Michael S. Branicky at Thu Mar 24 14:07:15 EDT 2022

EXAMPLE

256 -> 3600 -> 324 -> 576 -> 44100 -> 256 is a limit cycle of f, so all elements are terms.

#2 by Michael S. Branicky at Thu Mar 24 13:55:19 EDT 2022

NAME

allocated Positive integers that are fixed points for the map x->f^k(x) for Michael Ssome k>1, where f(x) is the product of squares of nonzero digits of x. Branicky

DATA

256, 324, 576, 3600, 11664, 15876, 20736, 44100, 63504, 65536, 129600, 2822400, 5308416, 7290000, 8294400

OFFSET

1,1

COMMENTS

f(x) = A352598(x).

Fixed points of f(x) are in A115385.

64524128256, 386983526400, 849346560000, 49787136000000, 55725627801600 are also terms.

PROG

(Python)

from math import prod

from itertools import count, islice

def f(n): return prod(int(d)**2 for d in str(n) if d != "0")

def ok(n):

n0, k, seen = n, 0, set(),

while n not in seen: # iterate until fixed point or in cycle

seen.add(n)

n = f(n)

k += 1

return n == n0 and k > 1

def agen(startk=1):

for m in count(1):

if ok(m): yield m

print(list(islice(agen(), 11))) # Michael S. Branicky, Mar 24 2022

CROSSREFS

Subsequence of the intersection of A000290 and A002473.

Cf. A115385, A351327, A352598.

KEYWORD

allocated

nonn

AUTHOR

Michael S. Branicky, Mar 24 2022

STATUS

approved

editing

#1 by Michael S. Branicky at Mon Mar 21 18:04:01 EDT 2022

NAME

allocated for Michael S. Branicky

KEYWORD

allocated

STATUS

approved