cp's OEIS Frontend

A075905 Numbers k such that k^5 has k as a substring of its representation.

%I A075905 #23 Jul 06 2025 10:14:59
%S A075905 0,1,2,3,4,5,6,7,8,9,10,18,20,24,25,30,32,40,43,45,48,49,50,51,57,60,
%T A075905 68,70,73,75,76,80,90,93,99,100,101,125,178,192,193,195,200,205,240,
%U A075905 249,250,251,300,307,320,375,376,400,430,432,443,480,490,499,500,501
%N A075905 Numbers k such that k^5 has k as a substring of its representation.
%H A075905 Chai Wah Wu, <a href="/A075905/b075905.txt">Table of n, a(n) for n = 1..1091</a>
%e A075905 45^5 = 18_45_28125, 3637^5 = 6_3637_9975073041957, 3975^5 = 992_3975_07802734375.
%t A075905 Select[Range[0,600],SequenceCount[IntegerDigits[#^5],IntegerDigits[#]]>0&] (* _Harvey P. Dale_, Jul 06 2025 *)
%o A075905 (Python)
%o A075905 A075905_list, m = [0], [120, -240, 150, -30, 1, 0]
%o A075905 for n in range(1,10**8+1):
%o A075905     for i in range(5):
%o A075905         m[i+1] += m[i]
%o A075905     if str(n) in str(m[-1]):
%o A075905         A075905_list.append(n) # _Chai Wah Wu_, Nov 05 2014
%Y A075905 Cf. A018834 (squares), A029942 (cubes), A075904 (4th powers).
%K A075905 base,nonn
%O A075905 1,3
%A A075905 _Zak Seidov_, Sep 27 2002