A084024 Triangle read by rows in which row n gives n smallest n-digit multiples of n that are palindromes with rows padded with 0 if there are insufficient palindromes.

1, 22, 44, 111, 141, 171, 2112, 2332, 2552, 2772, 50005, 50105, 50205, 50305, 50405, 201102, 204402, 207702, 210012, 213312, 216612, 1002001, 1009001, 1011101, 1018101, 1020201, 1027201, 1036301, 21100112, 21111112, 21122112, 21133112, 21144112, 21155112, 21166112, 21177112

Offset

1,2

Comments

When n is a multiple of 10 there are no solutions and a row of n zeros occurs. Are there any nontrivial zeros? - Sean A. Irvine, Mar 04 2026

Links

Table of n, a(n) for n=1..36.

Formula

T(n, 1) >= A053041(n); T(n, 1) = A083123(n). - Michel Marcus, Mar 28 2020

Example

Triangle begins:
     1;
    22,   44;
   111,  141,  171;
  2112, 2332, 2552, 2772;
  ...

Mathematica

snm[n_] := If[Divisible[n, 10], ConstantArray[0, n], Module[{a = 10^(n - 1), b = 10^n - 1}, Select[ Select[ Range[ a, b], Divisible[#, n] && IntegerLength[#] == n & ], PalindromeQ, n] ] ]; Array[snm, 7] // Flatten (* Harvey P. Dale, Aug 23 2020 *)

Prog

(PARI) isok(k, n) = my(d=digits(k*n)); (#d == n) && (Vecrev(d) == d);
row(n) = {my(v=vector(n), k = ceil(10^(n-1)/n)); for (i=1, n, while(! isok(k, n), k++); v[i] = k*n; k++; ); v; } \\ Michel Marcus, Mar 28 2020

Crossrefs

Cf. A053041, A083123, A084025, A084026, A084027, A084028.

Sequence in context: A071266 A038153 A033848 * A342171 A092328 A138869

Adjacent sequences: A084021 A084022 A084023 * A084025 A084026 A084027

Keyword

base,nonn,tabl

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 23 2003

Extensions

Corrected and extended by Ray Chandler, Jun 12 2003

More terms from Michel Marcus, Mar 28 2020

Escape clause added to name by Sean A. Irvine, Mar 04 2026

Status

approved