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

Author

Henry Bottomley, Feb 14 2000

Keywords

• nonn
• base

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)

Crossrefs

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

Programs

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

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

Extensions

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