This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A084007 #15 Mar 21 2025 03:17:28 %S A084007 6,9,33,66,99,333,666,999,3333,6666,9999,33333,66666,99999,333333, %T A084007 666666,999999,3333333,6666666,9999999,33333333,66666666,99999999, %U A084007 333333333,444444444,555555555,666666666,777777777,888888888,999999999 %N A084007 a(n) = A084006(n)^(1/2). %F A084007 Pattern exhibited by early terms does not continue without interruption. First disruption occurs at a(25)=444444444. Terms with k-digits exhibit the earlier pattern where (10^k-1)/9 is squarefree and k=9 is the first occurrence where (10^k-1)/9 is not squarefree. Others occur at k=18, 22, 27, 36, 42, 44, 45. - _Ray Chandler_, Aug 04 2003 %o A084007 (Python) %o A084007 from itertools import count, islice %o A084007 from math import prod, isqrt %o A084007 from sympy import factorint %o A084007 def A084007_gen(): # generator of terms %o A084007 for l in count(1): %o A084007 m = 10**l-1 %o A084007 x = prod(p for p, e in factorint(m).items() if e&1) %o A084007 y = isqrt(x*m) %o A084007 yield from (j*y for j in range(isqrt(10**(l-1)//x)+1,isqrt(m//x)+1)) %o A084007 A084007_list = list(islice(A084007_gen(),30)) # _Chai Wah Wu_, Mar 20 2025 %Y A084007 Cf. A084004, A084005, A084006. %K A084007 base,nonn %O A084007 0,1 %A A084007 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 23 2003 %E A084007 More terms from _Ray Chandler_, May 31 2003 %E A084007 More terms from _Ray Chandler_, Aug 04 2003