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A339676 Nonpalindromic numbers that are products of repunits. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A287297 A296117 A038681 * A017285 A017393 A017657

Adjacent sequences:  A339673 A339674 A339675 * A339677 A339678 A339679

KEYWORD

nonn,base

AUTHOR

Bernard Schott, Dec 12 2020

STATUS

approved

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Last modified June 15 19:31 EDT 2021. Contains 345049 sequences. (Running on oeis4.)