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

1,2

Comments

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

Links

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

Example

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.

Mathematica

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

Prog

(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++;
        }
    }
}
(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

Crossrefs

Cf. A007908, A030467, A259379.

Sequence in context: A235217 A236383 A224668 * A030467 A253505 A173798

Adjacent sequences: A343533 A343534 A343535 * A343537 A343538 A343539

Keyword

nonn,base

Author

John R Phelan, Apr 18 2021

Extensions

More terms from Jinyuan Wang, Apr 30 2021

Status

approved