A083145 Smallest nontrivial palindromic multiple of the n-th palindrome (a(n) is not equal to the n-th palindrome).

2, 4, 6, 8, 55, 66, 77, 88, 99, 22, 44, 66, 88, 5005, 858, 616, 616, 1881, 202, 222, 242, 262, 282, 1661, 1771, 1881, 1991, 19291, 404, 424, 444, 464, 484, 2772, 2882, 2992, 27072, 29492, 606, 626, 646, 666, 686, 3883, 3993, 37673, 38683, 14541, 808, 828

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Mathematica

spm[n_]:=Module[{k=2}, While[!PalindromeQ[n k], k++]; n k]; spm/@Select[ Range[ 500], PalindromeQ] (* Harvey P. Dale, Aug 01 2021 *)

Prog

(Python)
from itertools import count
def A083145(n):
    p = (c:=n+1-x)*x+int(str(c)[-2::-1] or 0) if n+1<(x:=10**(len(str(n+1>>1))-1))+(y:=10*x) else (c:=n+1-y)*y+int(str(c)[::-1] or 0)
    for i in count(n+2):
        if not (q:=(c:=i-x)*x+int(str(c)[-2::-1] or 0) if i<(x:=10**(len(str(i>>1))-1))+(y:=10*x) else (c:=i-y)*y+int(str(c)[::-1] or 0))%p:
            return q # Chai Wah Wu, Jul 11 2024

Crossrefs

Cf. A083146.

Sequence in context: A163502 A110995 A075401 * A085920 A228327 A081507

Adjacent sequences: A083142 A083143 A083144 * A083146 A083147 A083148

Keyword

base,nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 25 2003

Extensions

More terms from Franklin T. Adams-Watters, May 16 2006

Definition clarified by Harvey P. Dale, Aug 01 2021

Status

approved