A347402 Lexicographically earliest sequence of distinct terms > 0 such that the product n * a(n) forms a palindrome in base 10.

1, 2, 3, 11, 101, 37, 23, 29, 19, 0, 4, 21, 38, 18, 35, 17, 16, 14, 9, 0, 12, 22, 7, 88, 209, 26, 703, 31, 8, 0, 28, 66, 47, 121, 15, 77, 6, 13, 154, 0, 187, 143, 277, 48, 1129, 99, 33, 44, 239, 0, 291, 406, 132, 518, 91, 377, 303, 364, 219, 0, 442, 386, 287, 333, 777

Offset: 1

Author

Eric Angelini and Carole Dubois, Aug 30 2021

Keywords

• base
• nonn

Comments

When n ends with a zero, we have a(n) = 0 in the sequence.

Examples

			For n = 7 we have a(7) = 23 and 7 * 23 = 161 is a palindrome in base 10; indeed, at n=7, multiples 7 * 1 = 7 and 7 * 11 = 77 are palindromes but 1 and 11 have already appeared in the sequence. The next palindrome multiple is 7 * 23 = 161 and 23 has not yet appeared so a(7) = 23;
for n = 8 we have a(8) = 29 and 8 * 29 = 232 is a palindrome in base 10;
for n = 9 we have a(9) = 19 and 9 * 19 = 171 is a palindrome in base 10;
for n = 10 we have a(10) = 0 and 10 * 0 = 0 is a palindrome in base 10;
for n = 11 we have a(11) = 4 and 11 * 4 = 44 is a palindrome in base 10; etc.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A050782, A347335, A347336, A347400, A347401.

Programs

Mathematica

a[1]=1;a[n_]:=a[n]=If[Mod[n,10]==0,0,(k=1;While[!PalindromeQ[n*k]||MemberQ[Array[a,n-1],k],k++];k)];Array[a,65] (* Giorgos Kalogeropoulos, May 05 2022 *)

Python

def ispal(n): s = str(n); return s == s[::-1]
def aupton(terms):
    alst, seen = [1], {1}
    for n in range(2, terms+1):
        if n%10 == 0: alst.append(0); continue
        an = 1
        while an in seen or not ispal(n * an): an += 1
        alst.append(an); seen.add(an)
    return alst
print(aupton(100)) # Michael S. Branicky, Aug 30 2021