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

1,1

Links

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

Example

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

Prog

(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+1<x+y else (c:=n+1-y)*y+int(str(c)[::-1] or 0))
    return int(''.join('9753113579'[int(d)] for d in m)) # Chai Wah Wu, Jul 24 2024

Crossrefs

Cf. A002113, A061601.

Sequence in context: A199794 A106040 A320158 * A180597 A219242 A330920

Adjacent sequences: A085924 A085925 A085926 * A085928 A085929 A085930

Keyword

base,easy,nonn

Author

Amarnath Murthy and Jason Earls, Jul 13 2003

Extensions

Edited and extended by David Wasserman, Feb 11 2005

Status

approved