A334131 -id:A334131 - cp's OEIS frontend

A339676 Nonpalindromic numbers that are products of repunits.

161051, 1490841, 1625151, 1771561, 14921841, 15043941, 16266151, 16399251, 17876661, 19487171, 137009631, 149231841, 149352841, 150574941, 151807041, 162676151, 164140251, 165483351, 178927661, 180391761, 196643271, 214358881, 1370219631, 1371330631, 1492331841

Offset: 1

Bernard Schott, Dec 12 2020

The first term is A308365(19).

G. J. Simmons conjectured there are no palindromes of form n^k for k >= 5 (and n > 1) (see link, page 98). According to this conjecture, these perfect powers are terms: {11^k, k>=4}, {111^k, k>=4}, {1111^k, k>=3}, {11111^k, k>=3}, ...

			a(1) = 161051 = 11^5.
a(2) = 1490841 = 11^2 * 111^2.
a(3) = 1625151 = 11^4 * 111.
a(4) = 1771561 = 11^6.
a(5) = 14921841 = 11^2 * 111 * 1111.

David A. Corneth, Table of n, a(n) for n = 1..10000
Gustavus J. Simmons, Palindromic Powers, J. Rec. Math., 3 (No. 2, 1970), 93-98 [Annotated scanned copy].

Intersection of A308365 and A029742.

Cf. A083278, A334131.

vec[max_] := Module[{m = Floor @ Log10[9*max + 1], r, s = {1}, s1}, r = (10^Range[2, m] - 1)/9; Do[emax = Floor@Log[r[[k]], max]; s1 = r[[k]]^Range[0, emax]; s = Select[Union[Flatten[Outer[Times, s, s1]]], # <= max &], {k, 1, m - 1}]; s]; Select[vec[1.5*10^9], !PalindromeQ[#] &] (* Amiram Eldar, Dec 12 2020 *)

A334140 Numbers that can be written as a product of distinct palindromes.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 54, 55, 56, 60, 63, 64, 66, 70, 72, 77, 80, 84, 88, 90, 96, 99, 101, 105, 108, 110, 111, 112, 120, 121, 126, 131, 132, 135, 140

Offset: 1

Ilya Gutkovskiy, Apr 15 2020

David A. Corneth, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Palindromic Number
Index entries for sequences related to palindromes

Cf. A002113, A033620, A084034, A115683, A140332, A334131.

ok[n_, w_: {}] := n <= 1 || AnyTrue[ Divisors@ n, ! MemberQ[w, #] && PalindromeQ[#] && ok[n/#, Append[w, #]] &]; Select[Range[0, 140], ok] (* Giovanni Resta, Apr 15 2020 *)

cp's OEIS Frontend

A339676 Nonpalindromic numbers that are products of repunits.

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