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Repunit powers.
7

%I #17 May 29 2019 15:29:16

%S 1,11,111,121,1111,1331,11111,12321,14641,111111,161051,1111111,

%T 1234321,1367631,1771561,11111111,19487171,111111111,123454321,

%U 151807041,214358881,1111111111,1371330631,2357947691,11111111111

%N Repunit powers.

%H Reinhard Zumkeller, <a href="/A083278/b083278.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Repunit">Repunit</a>

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

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

%o (Haskell)

%o import Data.Set (empty, findMin, deleteMin, deleteMin, insert)

%o import qualified Data.Set as Set (null)

%o a083278 n = a083278_list !! (n-1)

%o a083278_list = 1 : f empty (drop 2 a002275_list) where

%o f rups rus'@(ru:rus)

%o | Set.null rups || m > ru = f (insert (ru,ru) rups) rus

%o | otherwise = m : f (insert (m*m',m') (deleteMin rups)) rus'

%o where (m,m') = findMin rups

%o -- _Reinhard Zumkeller_, Feb 05 2012

%o (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

%Y Cf. A002275, A206245.

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, Jun 02 2003