A083278 Repunit powers.

1, 11, 111, 121, 1111, 1331, 11111, 12321, 14641, 111111, 161051, 1111111, 1234321, 1367631, 1771561, 11111111, 19487171, 111111111, 123454321, 151807041, 214358881, 1111111111, 1371330631, 2357947691, 11111111111

Offset: 1

Author

Reinhard Zumkeller, Jun 02 2003

Keywords

• nonn
• base

Examples

			a(13)=1234321=1111^2; a(14)=1367631=111^3; a(15)=1771561=11^6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Repunit
• Wikipedia, Repunit

Crossrefs

Cf. A002275, A206245.

Programs

Haskell

import Data.Set (empty, findMin, deleteMin, deleteMin, insert)
import qualified Data.Set as Set (null)
a083278 n = a083278_list !! (n-1)
a083278_list = 1 : f empty (drop 2 a002275_list) where
   f rups rus'@(ru:rus)
     | Set.null rups || m > ru = f (insert (ru,ru) rups) rus
     | otherwise = m : f (insert (m*m',m') (deleteMin rups)) rus'
     where (m,m') = findMin rups
-- Reinhard Zumkeller, Feb 05 2012

Mathematica

With[{intlen=12},Select[Union[Flatten[#^Range[intlen]&/@(FromDigits/@ Table[ PadRight[{},n,1],{n,intlen}])]],IntegerLength[#]<=intlen&]] (* Harvey P. Dale, Apr 25 2016 *)

PARI

lista(nn) = {my(list = List(), r); for (n=1, nn, my(r = (10^n-1)/9); listput(list, r); if (r > 1, my(e=2); while(#Str(x=r^e) <= nn, listput(list, x); e++));); Vec(vecsort(list));} \\ Michel Marcus, May 28 2019