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A083278 Repunit powers.

%I A083278 #18 Feb 16 2025 08:32:49
%S A083278 1,11,111,121,1111,1331,11111,12321,14641,111111,161051,1111111,
%T A083278 1234321,1367631,1771561,11111111,19487171,111111111,123454321,
%U A083278 151807041,214358881,1111111111,1371330631,2357947691,11111111111
%N A083278 Repunit powers.
%H A083278 Reinhard Zumkeller, <a href="/A083278/b083278.txt">Table of n, a(n) for n = 1..1000</a>
%H A083278 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repunit.html">Repunit</a>
%H A083278 Wikipedia, <a href="http://en.wikipedia.org/wiki/Repunit">Repunit</a>
%e A083278 a(13)=1234321=1111^2; a(14)=1367631=111^3; a(15)=1771561=11^6.
%t A083278 With[{intlen=12},Select[Union[Flatten[#^Range[intlen]&/@(FromDigits/@ Table[ PadRight[{},n,1],{n,intlen}])]],IntegerLength[#]<=intlen&]] (* _Harvey P. Dale_, Apr 25 2016 *)
%o A083278 (Haskell)
%o A083278 import Data.Set (empty, findMin, deleteMin, deleteMin, insert)
%o A083278 import qualified Data.Set as Set (null)
%o A083278 a083278 n = a083278_list !! (n-1)
%o A083278 a083278_list = 1 : f empty (drop 2 a002275_list) where
%o A083278    f rups rus'@(ru:rus)
%o A083278      | Set.null rups || m > ru = f (insert (ru,ru) rups) rus
%o A083278      | otherwise = m : f (insert (m*m',m') (deleteMin rups)) rus'
%o A083278      where (m,m') = findMin rups
%o A083278 -- _Reinhard Zumkeller_, Feb 05 2012
%o A083278 (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 A083278 Cf. A002275, A206245.
%K A083278 nonn,base
%O A083278 1,2
%A A083278 _Reinhard Zumkeller_, Jun 02 2003