A397524

Numbers k such that the sums of the digits of k^2, k^3 and k^4 coincide, excluding multiples of 10.

Created: 7/17/2026 | Author: Vincenzo Manto , Jun 29 2026

This sequence has been cited by and influenced 1 other sequence

Official Comments

While the sequence of numbers k such that the sums of the digits of k^2, k^3 and k^4 coincide is infinite, since it is always possible to append zeros to obtain a new term, it is not known whether there are an infinite number of terms without trailing zeros (when excluding multiples of 10, A008592).
For any term k, k^2 == k^3 == k^4 (mod 9), which implies that k mod 9 must belong to {0, 1, 3, 6}.

Sequence Chart

Data

1,3,93,219,267,387,685,1333,2814,2973,6723,9807,10173,10293,10333,10917,12234,13167,21786,22113,22167,23643,24114,24183,25093,30387,30817,35623,39861,40986,41712,43417,51864,53193,53754,56565,59757,60537,60564,62007,62343

Computational Implementations

PYTHON

def ok(k):
    return k % 10 != 0 and sum(map(int, str(k**2))) == sum(map(int, str(k**3))) == sum(map(int, str(k**4)))
print([k for k in range(1, 70000) if ok(k)])

CODE

\\ See Corneth link

Mathematica

Select[Range[70000], Mod[#, 10] != 0 && DigitSum[#^2] == DigitSum[#^3] == DigitSum[#^4] &] (* _Stefano Spezia_, Jun 30 2026 *)