A053701 Vertically symmetric numbers.

0, 1, 8, 11, 25, 52, 88, 101, 111, 181, 205, 215, 285, 502, 512, 582, 808, 818, 888, 1001, 1111, 1251, 1521, 1881, 2005, 2115, 2255, 2525, 2885, 5002, 5112, 5252, 5522, 5882, 8008, 8118, 8258, 8528, 8888, 10001, 10101, 10801, 11011, 11111, 11811

Offset

1,3

Comments

Numbers that are symmetric about a vertical mirror.

2 and 5 are taken as mirror images (as on calculator displays).

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Nathaniel Johnston)

Maple

compdig := proc(n) if(n=2)then return 5: elif(n=5)then return 2: elif(n=0 or n=1 or n=8)then return n: else return -1: fi: end: isA053701 := proc(n) local d, l, j: d:=convert(n, base, 10): l:=nops(d): for j from 1 to ceil(l/2) do if(not d[j]=compdig(d[l-j+1]))then return false: fi: od: return true: end: for n from 0 to 10000 do if(isA053701(n))then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 17 2011

Prog

(Python)
from itertools import count, islice, product
def lr(s): return s[::-1].translate({ord('2'):ord('5'), ord('5'):ord('2')})
def A053701gen(): # generator of terms
    yield from [0, 1, 8]
    for d in count(2):
        for first in "1258":
            for rest in product("01258", repeat=d//2-1):
                left = first + "".join(rest)
                for mid in [[""], ["0", "1", "8"]][d%2]:
                    yield int(left + mid + lr(left))
print(list(islice(A053701gen(), 45))) # Michael S. Branicky, Jul 09 2022

Crossrefs

Cf. A000787, A007284, A018846 (strobogrammatic numbers).

Sequence in context: A291664 A318347 A195160 * A029615 A051791 A243975

Adjacent sequences: A053698 A053699 A053700 * A053702 A053703 A053704

Keyword

nonn,base

Author

Henry Bottomley, Feb 14 2000

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Oct 01 2001

Status

approved