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

1,3

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A035111 A035282 A075156 * A018834 A029943 A356760

Adjacent sequences: A075901 A075902 A075903 * A075905 A075906 A075907

Keyword

base,nonn

Author

Zak Seidov, Sep 27 2002

Extensions

More terms from Tanya Khovanova, Oct 11 2007

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

Status

approved