A085927 - OEIS

%I #19 Jul 24 2024 15:18:17

%S 7,5,3,1,1,3,5,7,9,77,55,33,11,11,33,55,77,99,797,777,757,737,717,717,

%T 737,757,777,797,595,575,555,535,515,515,535,555,575,595,393,373,353,

%U 333,313,313,333,353,373,393,191,171,151,131,111,111,131,151,171,191

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

%H Michael S. Branicky, <a href="/A085927/b085927.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (Python)

%o from sympy import isprime

%o from itertools import count, product

%o def f(s): return int("".join(str(abs(9 - 2*int(c))) for c in s))

%o def pals(base=10): # all (nonzero) palindromes as strings

%o     digits = "".join(str(i) for i in range(base))

%o     for d in count(1):

%o         for p in product(digits, repeat=d//2):

%o             if d > 1 and p[0] == "0": continue

%o             left = "".join(p); right = left[::-1]

%o             for mid in [[""], digits][d%2]:

%o                 t = left + mid + right

%o                 if t != '0': yield t

%o def aupton(nn): p = pals(); return [f(next(p)) for i in range(nn)]

%o print(aupton(58)) # _Michael S. Branicky_, Jul 05 2021

%o (Python)

%o def A085927(n):

%o     y = 10*(x:=10**(len(str(n+1>>1))-1))

%o     m = str((c:=n+1-x)*x+int(str(c)[-2::-1] or 0) if n+1<x+y else (c:=n+1-y)*y+int(str(c)[::-1] or 0))

%o     return int(''.join('9753113579'[int(d)] for d in m)) # _Chai Wah Wu_, Jul 24 2024

%Y Cf. A002113, A061601.

%K base,easy,nonn

%O 1,1

%A _Amarnath Murthy_ and _Jason Earls_, Jul 13 2003

%E Edited and extended by _David Wasserman_, Feb 11 2005