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

1,2

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

Cf. A005349, A002473.

Sequence in context: A235507 A235697 A085135 * A308560 A285815 A337741

Adjacent sequences: A085130 A085131 A085132 * A085134 A085135 A085136

Keyword

base,nonn

Author

Amarnath Murthy, Jul 06 2003

Extensions

More terms from David Wasserman, Jan 28 2005

Status

approved