login
Numbers which are products of repunits.
4

%I #73 Jan 17 2022 10:03:10

%S 1,11,111,121,1111,1221,1331,11111,12221,12321,13431,14641,111111,

%T 122221,123321,134431,135531,147741,161051,1111111,1222221,1233321,

%U 1234321,1344431,1356531,1367631,1478741,1490841,1625151,1771561,11111111,12222221,12333321

%N Numbers which are products of repunits.

%C The number of terms below 10^n is A216053(n)-1 for 1 <= n <= 25, but not for larger n. - _Rémy Sigrist_, May 28 2019

%C The product of repunits is not necessarily palindromic, see A339676. - _Bernard Schott_, Apr 02 2021

%H Robert Israel, <a href="/A308365/b308365.txt">Table of n, a(n) for n = 1..10000</a>

%e a(11) = 13431 is in the sequence since it is the product of repunits (11^2*111).

%p d:= 10: # for terms < 10^d

%p N:= 10^d:

%p S:= {1}:

%p for m from 2 to d do

%p r:= (10^m-1)/9;

%p k:= floor(log[r](N));

%p V:= S;

%p for i from 1 to k do

%p V:= select(`<`,map(`*`,V,r),N);

%p S:= S union V

%p od;

%p od:

%p sort(convert(S,list)); # _Robert Israel_, Nov 26 2020

%Y Cf. A002275 (repunits), A083278 (repunit powers), A216053, A339676 (nonpalindromic terms).

%K nonn,base

%O 1,2

%A _Sergio Pimentel_, May 22 2019

%E Missing a(25) = 1356531 inserted by _Ilya Gutkovskiy_, Apr 14 2020