A308365 Numbers which are products of repunits.

1, 11, 111, 121, 1111, 1221, 1331, 11111, 12221, 12321, 13431, 14641, 111111, 122221, 123321, 134431, 135531, 147741, 161051, 1111111, 1222221, 1233321, 1234321, 1344431, 1356531, 1367631, 1478741, 1490841, 1625151, 1771561, 11111111, 12222221, 12333321

Offset: 1

Author

Sergio Pimentel, May 22 2019

Keywords

• nonn
• base

Comments

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

The product of repunits is not necessarily palindromic, see A339676. - Bernard Schott, Apr 02 2021

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Maple

d:= 10: # for terms < 10^d
N:= 10^d:
S:= {1}:
for m from 2 to d do
  r:= (10^m-1)/9;
  k:= floor(log[r](N));
  V:= S;
  for i from 1 to k do
    V:= select(`<`,map(`*`,V,r),N);
    S:= S union V
  od;
od:
sort(convert(S,list)); # Robert Israel, Nov 26 2020

Extensions

Missing a(25) = 1356531 inserted by Ilya Gutkovskiy, Apr 14 2020