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A053701
Vertically symmetric numbers.
12
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
KEYWORD
nonn,base
AUTHOR
Henry Bottomley, Feb 14 2000
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Oct 01 2001
STATUS
approved