A085133 Numbers k such that k and its digit reversal are both 7-smooth (A002473).

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

Author

Amarnath Murthy, Jul 06 2003

Keywords

• base
• nonn

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)

Crossrefs

Cf. A005349, A002473.

Programs

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

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

Extensions

More terms from David Wasserman, Jan 28 2005