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%I #41 Jul 28 2021 04:17:38
%S 428,573,727,846,7810,36365,63636,326734,673267,4545454,5454547,
%T 47058823,52941178,331983807,332667334,384615386,422892898,475524477,
%U 524475524,577107103,615384615,667332667,668016194,719964246,758241758,804511280,810873337,857142859
%N Numbers k such that k^2 is a concatenation of two successive numbers.
%H Chai Wah Wu, <a href="/A030467/b030467.txt">Table of n, a(n) for n = 1..10471</a> (terms n = 1..53 from Donovan Johnson, terms n = 54..1000 from Giovanni Resta)
%H Pante Stanica, <a href="https://wcnt.files.wordpress.com/2017/12/wcnt2017-pante.pdf">Squares as concatenation of consecutive integers</a>, Slides, West Coast Number Theory, Dec 17 2017.
%e 428^2 = 183184, the concatenation of 183 and 184.
%t t={}; Do[If[EvenQ[y=Length[x=IntegerDigits[n^2]]] && Differences[FromDigits/@Partition[x,y/2]]=={1},AppendTo[t,n]],{n, 5.5*10^6}]; t (* _Jayanta Basu_, May 25 2013 *)
%t Sqrt[#]&/@(Select[FromDigits[Flatten[IntegerDigits/@#]]&/@ (Partition[ Range[735*10^6],2,1]),IntegerQ[Sqrt[#]]&]) (* The program takes a long time to run. *) (* _Harvey P. Dale_, Oct 10 2017 *)
%o (PARI) for(n=1, 10^9, t=eval(concat(Str(n),Str(n+1))); if(issquare(t,&s), print1(s,", "))); /* _Antonio Roldán_ and _Joerg Arndt_, Dec 31 2012 */
%Y Cf. A030465, A030466, A054214, A054215, A054216, A020339, A020340.
%K nonn,base,nice
%O 1,1
%A _Patrick De Geest_
%E a(17) corrected by _Donovan Johnson_, Jan 03 2013
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