A085927 a(n) is the digitwise absolute difference between the n-th palindrome and its 9's complement.

7, 5, 3, 1, 1, 3, 5, 7, 9, 77, 55, 33, 11, 11, 33, 55, 77, 99, 797, 777, 757, 737, 717, 717, 737, 757, 777, 797, 595, 575, 555, 535, 515, 515, 535, 555, 575, 595, 393, 373, 353, 333, 313, 313, 333, 353, 373, 393, 191, 171, 151, 131, 111, 111, 131, 151, 171, 191

Offset: 1

Author

Amarnath Murthy and Jason Earls, Jul 13 2003

Keywords

• base
• easy
• nonn

Examples

			a(24) = 717 because A002113(24) = 151 and A061601(151) = 848. 8-1 = 7 and 5-4 = 1, thus 717.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002113, A061601.

Programs

Python

from sympy import isprime
from itertools import count, product
def f(s): return int("".join(str(abs(9 - 2*int(c))) for c in s))
def pals(base=10): # all (nonzero) palindromes as strings
    digits = "".join(str(i) for i in range(base))
    for d in count(1):
        for p in product(digits, repeat=d//2):
            if d > 1 and p[0] == "0": continue
            left = "".join(p); right = left[::-1]
            for mid in [[""], digits][d%2]:
                t = left + mid + right
                if t != '0': yield t
def aupton(nn): p = pals(); return [f(next(p)) for i in range(nn)]
print(aupton(58)) # Michael S. Branicky, Jul 05 2021

Python

def A085927(n):
    y = 10*(x:=10**(len(str(n+1>>1))-1))
    m = str((c:=n+1-x)*x+int(str(c)[-2::-1] or 0) if n+1Chai Wah Wu, Jul 24 2024

Extensions

Edited and extended by David Wasserman, Feb 11 2005