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

1, 428, 573, 725, 727, 738, 846, 7810, 8093, 28023, 36354, 36365, 36464, 63636, 254544, 277851, 297422, 326734, 673267, 673368, 2889810, 4545454, 4545465, 5454547, 5454646, 24275425, 29411775, 47058823, 52941178, 94117748, 146407310, 263157795, 267735365, 285714186

Offset: 1

Author

John R Phelan, Apr 18 2021

Keywords

• nonn
• base

Comments

A030467 is a subsequence. - Chai Wah Wu, Jun 07 2021

Examples

			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.
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.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..116

Crossrefs

Cf. A007908, A030467, A259379.

Programs

Java

public class Oeis2 {
    public static void main(String[] args) {
        StringBuilder str = new StringBuilder();
        long n = 1;
        while (true) {
            str.append(n);
            if (str.indexOf(String.valueOf(n * n)) >= 0) {
                System.out.print(n + ", ");
            }
            n++;
        }
    }
}

Mathematica

Select[Range@1000,StringContainsQ[""<>ToString/@Range@#,ToString[#^2]]&] (* Giorgos Kalogeropoulos, Apr 24 2021 *)
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 *)

PARI

f(n) = my(s=""); for(k=1, n, s=Str(s, k)); s; \\ from A007908
isok(k) = #strsplit(f(k), Str(k^2)) > 1; \\ Michel Marcus, May 02 2021

Python

A343536_list, k, s = [], 1, '1'
while k < 10**6:
    if str(k**2) in s:
        A343536_list.append(k)
    k += 1
    s += str(k) # Chai Wah Wu, Jun 06 2021

Extensions

More terms from Jinyuan Wang, Apr 30 2021