A075904 Numbers k such that k^4 has k as a substring of its decimal expansion.

0, 1, 5, 6, 10, 25, 50, 60, 76, 83, 92, 100, 107, 211, 217, 250, 352, 363, 376, 500, 556, 600, 625, 636, 760, 863, 909, 935, 1000, 1531, 1636, 2263, 2500, 2503, 3630, 3760, 4342, 5000, 5001, 6000, 6250, 7245, 7600, 8578, 9350, 9376, 10000, 25000, 28206, 32213

Offset: 1

Author

Zak Seidov, Sep 27 2002

Keywords

• base
• nonn

Examples

			6^4 = 129_6, 83^4 = 4745_83_21, 2503^4 = 39_2503_37770081.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..206

Crossrefs

Cf. A018834 (squares), A029942 (cubes), A075905 (5th powers).

Programs

Mathematica

Select[Range[10000], StringPosition[ToString[ #^4], ToString[ # ]] != {} &] (* Tanya Khovanova, Oct 11 2007 *)
ssQ[n_]:=Module[{idn=IntegerDigits[n],idn4=IntegerDigits[n^4]}, MemberQ[ Partition[ idn4, Length[ idn],1], idn]]; Select[Range[10000],ssQ] (* Harvey P. Dale, Mar 13 2013 *)

Python

A075904_list, m = [0], [24, -36, 14, -1, 0]
for n in range(1,10**9+1):
    for i in range(4):
        m[i+1] += m[i]
    if str(n) in str(m[-1]):
        A075904_list.append(n) # Chai Wah Wu, Nov 05 2014

Extensions

More terms from Tanya Khovanova, Oct 11 2007

Added 0 to sequence by Chai Wah Wu, Nov 05 2014