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URL: https://oeis.org/A085133

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A085133
Numbers k such that k and its digit reversal are both 7-smooth (A002473).
2
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 120, 144, 180, 200, 210, 240, 252, 270, 288, 300, 343, 360, 400, 405, 420, 441, 450, 480, 500, 504, 525, 540, 576, 600, 630, 675, 686, 700, 720
OFFSET
1,2
COMMENTS
Though a large number of initial terms match, it is different from A005349.
From Robert Israel, Mar 18 2018: (Start)
If n is a term, then so are 10^k*n for all k.
Is a(147)=84672 the last term not divisible by 10? If so, then a(n+43)=10*a(n) for n >= 105. (End)
All terms a(147..10000) are divisible by 10; a(10000) has 235 decimal digits. - Michael S. Branicky, Sep 21 2024
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1225 from Robert Israel)
MAPLE
N:= 10^3: # to get all terms <= N (which should be a power of 10)
revdigs:= proc(n) local L;
L:= convert(n, base, 10);
add(10^(i-1)*L[-i], i=1..nops(L))
end proc:
S:= {seq(seq(seq(seq(2^a*3^b*5^c*7^d, d=0..floor(log[7](N/(2^a*3^b*5^c)))), c=0..floor(log[5](N/(2^a*3^b)))), b=0..floor(log[3](N/2^a))), a=0..floor(log[2](N)))}:
S:= S intersect map(revdigs, S):
S:= map(t -> seq(t*10^i, i=0..ilog10(N/t)), S):
sort(convert(S, list)); # Robert Israel, Mar 18 2018
PROG
(Python)
import heapq
from itertools import islice
from sympy import factorint
def is7smooth(n):
for p in [2, 3, 5, 7]:
while n%p == 0: n //= p
return n == 1
def agen(): # generator of terms
v, oldv, h = 1, 0, [1]
while True:
v = heapq.heappop(h)
if v != oldv:
if is7smooth(int(str(v)[::-1])):
yield v
oldv = v
for p in [2, 3, 5, 7]:
heapq.heappush(h, v*p)
print(list(islice(agen(), 65))) # Michael S. Branicky, Sep 20 2024
CROSSREFS
Sequence in context: A235507 A235697 A085135 * A308560 A285815 A337741
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Jul 06 2003
EXTENSIONS
More terms from David Wasserman, Jan 28 2005
STATUS
approved