A259379 -id:A259379 - cp's OEIS frontend

A260193 Numbers k of the form abs(a - b + c - d) such that k^4 equals the concatenation of a//b//c//d and numbers k,b,c,d have the same number of digits.

198, 220, 221, 287, 352, 364, 484, 562, 627, 638, 672, 715, 716, 780, 793, 858, 901, 1095, 1233, 2328, 8905, 18183, 39753, 60248, 85207, 336734, 2727274, 5893504, 8620777, 17769557, 52818678, 70710735, 76470590, 82230444, 101318734, 101636206, 104263158, 105262158, 109891110, 109942690, 117883117, 119722383, 120826541

Offset: 1

Pieter Post, Jul 22 2015

Leading zeros in b, c, and d are allowed.
Many numbers come in pairs, like: (220, 221), (715, 716), (140017877, 140017878).
Some numbers are also member of A259379, for example: 287, 715, 1095 and also the pair (140017877, 140017878).

			198^4 = 1536953616 and 198 = abs (1 - 536 + 953 - 616 ).
8905^4 = 6288335365950625 and 8905 = abs (6288 - 3353 + 6595 - 0625 ).

Pieter Post, Table of n, a(n) for n = 1..239

Cf. A056733, A101311, A118937, A118938, A228381, A257796, A258482, A259379.

test[n_] := Block[{L=IntegerLength@ n, v}, v = IntegerDigits[ n^4, 10^L]; Length@ v == 4 && Abs@ Total[ {1, -1, 1, -1} v] == n]; Select[Range[10^5], test] (* Giovanni Resta, Aug 12 2015 *)

def modb(n, m):
    kk = 0
    l = 1
    while n > 0:
        na = n % m
        l += 1
        kk += ((-1)**l) * na
        n //= m
    return abs(kk)
for n in range (100, 10**9):
    ll = len(str(n))
    if modb(n**4, 10**ll) == n and n**4 >= 10**(ll*3):
         print (n, end=', ') # corrected by David Radcliffe, May 09 2025

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

Original entry on oeis.org

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

John R Phelan, Apr 18 2021

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

			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.

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

Cf. A007908, A030467, A259379.

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++;
        }
    }
}

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 *)

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

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

More terms from Jinyuan Wang, Apr 30 2021

cp's OEIS Frontend

A260193 Numbers k of the form abs(a - b + c - d) such that k^4 equals the concatenation of a//b//c//d and numbers k,b,c,d have the same number of digits.

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