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

1,2

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

Links

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

Example

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

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

Crossrefs

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

Sequence in context: A358441 A135464 A231872 * A083278 A039987 A039989

Adjacent sequences: A308362 A308363 A308364 * A308366 A308367 A308368

Keyword

nonn,base

Author

Sergio Pimentel, May 22 2019

Extensions

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

Status

approved