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A343536 Positive numbers k such that the decimal expansion of k^2 appears in the concatenation of the first k positive integers.

%I A343536 #61 Jul 06 2025 17:58:19
%S A343536 1,428,573,725,727,738,846,7810,8093,28023,36354,36365,36464,63636,
%T A343536 254544,277851,297422,326734,673267,673368,2889810,4545454,4545465,
%U A343536 5454547,5454646,24275425,29411775,47058823,52941178,94117748,146407310,263157795,267735365,285714186
%N A343536 Positive numbers k such that the decimal expansion of k^2 appears in the concatenation of the first k positive integers.
%C A343536 A030467 is a subsequence. - _Chai Wah Wu_, Jun 07 2021
%H A343536 Chai Wah Wu, <a href="/A343536/b343536.txt">Table of n, a(n) for n = 1..116</a>
%e A343536 428^2 = 183184, which appears in the concatenation of the first 428 positive integers at 183,184, i.e., (183184), so 428 is a term.
%e A343536 725^2 = 525625, which appears in the concatenation of the first 725 positive integers at 255,256,257, i.e., 25(525625)7, so 725 is a term.
%t A343536 Select[Range@1000,StringContainsQ[""<>ToString/@Range@#,ToString[#^2]]&] (* _Giorgos Kalogeropoulos_, Apr 24 2021 *)
%t A343536 Select[Range[68*10^4],SequenceCount[Flatten[IntegerDigits/@Range[#]],IntegerDigits[#^2]]>0&] (* The program generates the first 20 terms of the sequence. *) (* _Harvey P. Dale_, Jul 06 2025 *)
%o A343536 (Java)
%o A343536 public class Oeis2 {
%o A343536     public static void main(String[] args) {
%o A343536         StringBuilder str = new StringBuilder();
%o A343536         long n = 1;
%o A343536         while (true) {
%o A343536             str.append(n);
%o A343536             if (str.indexOf(String.valueOf(n * n)) >= 0) {
%o A343536                 System.out.print(n + ", ");
%o A343536             }
%o A343536             n++;
%o A343536         }
%o A343536     }
%o A343536 }
%o A343536 (PARI) f(n) = my(s=""); for(k=1, n, s=Str(s, k)); s; \\ from A007908
%o A343536 isok(k) = #strsplit(f(k), Str(k^2)) > 1; \\ _Michel Marcus_, May 02 2021
%o A343536 (Python)
%o A343536 A343536_list, k, s = [], 1, '1'
%o A343536 while k < 10**6:
%o A343536     if str(k**2) in s:
%o A343536         A343536_list.append(k)
%o A343536     k += 1
%o A343536     s += str(k) # _Chai Wah Wu_, Jun 06 2021
%Y A343536 Cf. A007908, A030467, A259379.
%K A343536 nonn,base
%O A343536 1,2
%A A343536 _John R Phelan_, Apr 18 2021
%E A343536 More terms from _Jinyuan Wang_, Apr 30 2021