A329254 Smallest palindrome k, not less than n, such that k is also a palindrome in base n.

1, 3, 4, 5, 6, 7, 8, 9, 191, 11, 232, 181, 222, 323, 828, 353, 252, 171, 666, 252, 22, 161, 737, 525, 494, 989, 252, 232, 929, 434, 1551, 33, 272, 525, 252, 111, 494, 585, 5775, 656, 252, 989, 44, 585, 414, 141, 2112, 343, 3333, 969, 676, 212, 5885, 55, 616

Offset

1,2

Comments

a(10^k) = 10^k+1 for k > 0. Conjecture: a(n) in base n has 3 or fewer digits. - Chai Wah Wu, Nov 17 2019

Links

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

Example

For n=9, 191_10 = 232_9.

Mathematica

Flatten@{1, Table[k = n; While[! PalindromeQ[k] || k != IntegerReverse[k, n], k++ ]; k, {n, 2, 200}]}

Prog

(PARI) ispal(k, b) = { my(d=digits(k, b)); d == Vecrev(d); }
a(n) = {if (n == 1, return(1)); my(k=n); while (!ispal(k, 10) || ! ispal(k, n), k++); k; } \\ Michel Marcus, Nov 18 2019

Crossrefs

Cf. A002113 (palindromes in base 10).

Sequence in context: A037351 A293727 A077528 * A359003 A183296 A138928

Adjacent sequences: A329251 A329252 A329253 * A329255 A329256 A329257

Keyword

nonn,base

Author

Robert Price, Nov 09 2019

Status

approved