cp's OEIS Frontend

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.

A273233 Squares that remain squares if you decrease them by 7 times a repunit with the same number of digits.

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%I A273233 #12 May 21 2016 22:43:39
%S A273233 81,841,7921,77841,790321,863041,982081,9991921,79014321,80299521,
%T A273233 94653441,7901254321,8635799041,778133930161,790123654321,
%U A273233 794396081521,816057482881,965485073281,989863816561,79012347654321,86358529399041,857789228465521,7901234587654321,8547733055510401
%N A273233 Squares that remain squares if you decrease them by 7 times a repunit with the same number of digits.
%C A273233 Any number ends in 1.
%H A273233 Giovanni Resta, <a href="/A273233/b273233.txt">Table of n, a(n) for n = 1..10000</a>
%e A273233 81 - 7*11 = 4 = 2^2;
%e A273233 841 - 7*111 = 64 = 8^2;
%e A273233 7921 - 7*1111 = 144 = 12^2.
%p A273233 P:=proc(q,h) local n; for n from 1 to q do
%p A273233 if type(sqrt(n^2-h*(10^(ilog10(n^2)+1)-1)/9),integer) then print(n^2);
%p A273233 fi; od; end: P(10^9,7);
%t A273233 sol[k_] := Block[{x, e = IntegerLength@k, d = Divisors@ k}, Union[ #+k/# & /@ Select[ Take[d, Ceiling[ Length@d/2]], EvenQ[x = #+k/#] && IntegerLength[ x^2/4] == e &]]^2/4]; r[n_] := 7 (10^n-1)/9; Flatten[sol /@ r /@ Range[12]] (* _Giovanni Resta_, May 18 2016 *)
%Y A273233 Cf. A002275, A061844, A273299-A273232, A273234.
%K A273233 nonn,easy,base
%O A273233 1,1
%A A273233 _Paolo P. Lava_, May 18 2016