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

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, 68, 70, 73, 75, 76, 80, 90, 93, 99, 100, 101, 125, 178, 192, 193, 195, 200, 205, 240, 249, 250, 251, 300, 307, 320, 375, 376, 400, 430, 432, 443, 480, 490, 499, 500, 501

Offset: 1

Author

Zak Seidov, Sep 27 2002

Keywords

• base
• nonn

Examples

			45^5 = 18_45_28125, 3637^5 = 6_3637_9975073041957, 3975^5 = 992_3975_07802734375.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1091

Crossrefs

Cf. A018834 (squares), A029942 (cubes), A075904 (4th powers).

Programs

Mathematica

Select[Range[0,600],SequenceCount[IntegerDigits[#^5],IntegerDigits[#]]>0&] (* Harvey P. Dale, Jul 06 2025 *)

Python

A075905_list, m = [0], [120, -240, 150, -30, 1, 0]
for n in range(1,10**8+1):
    for i in range(5):
        m[i+1] += m[i]
    if str(n) in str(m[-1]):
        A075905_list.append(n) # Chai Wah Wu, Nov 05 2014