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

1,1

Comments

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}, ...

Links

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].

Example

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.

Mathematica

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 *)

Crossrefs

Intersection of A308365 and A029742.

Cf. A083278, A334131.

Sequence in context: A296117 A176770 A038681 * A017285 A017393 A017657

Adjacent sequences: A339673 A339674 A339675 * A339677 A339678 A339679

Keyword

nonn,base

Author

Bernard Schott, Dec 12 2020

Status

approved