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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. 1

%I #59 Jun 09 2021 02:42:29

%S 1,428,573,725,727,738,846,7810,8093,28023,36354,36365,36464,63636,

%T 254544,277851,297422,326734,673267,673368,2889810,4545454,4545465,

%U 5454547,5454646,24275425,29411775,47058823,52941178,94117748,146407310,263157795,267735365,285714186

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

%C A030467 is a subsequence. - _Chai Wah Wu_, Jun 07 2021

%H Chai Wah Wu, <a href="/A343536/b343536.txt">Table of n, a(n) for n = 1..116</a>

%e 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 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 Select[Range@1000,StringContainsQ[""<>ToString/@Range@#,ToString[#^2]]&] (* _Giorgos Kalogeropoulos_, Apr 24 2021 *)

%o (Java)

%o public class Oeis2 {

%o public static void main(String[] args) {

%o StringBuilder str = new StringBuilder();

%o long n = 1;

%o while (true) {

%o str.append(n);

%o if (str.indexOf(String.valueOf(n * n)) >= 0) {

%o System.out.print(n + ", ");

%o }

%o n++;

%o }

%o }

%o }

%o (PARI) f(n) = my(s=""); for(k=1, n, s=Str(s, k)); s; \\ from A007908

%o isok(k) = #strsplit(f(k), Str(k^2)) > 1; \\ _Michel Marcus_, May 02 2021

%o (Python)

%o A343536_list, k, s = [], 1, '1'

%o while k < 10**6:

%o if str(k**2) in s:

%o A343536_list.append(k)

%o k += 1

%o s += str(k) # _Chai Wah Wu_, Jun 06 2021

%Y Cf. A007908, A030467, A259379.

%K nonn,base

%O 1,2

%A _John R Phelan_, Apr 18 2021

%E More terms from _Jinyuan Wang_, Apr 30 2021

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)