A103173
Numbers k such that the decimal digits of k are not present in k^2, k^3, or k^4.
Original entry on oeis.org
2, 3, 7, 8, 53, 77
Offset: 1
For k=77, the 1st through 4th powers are {77, 5929, 456533, 35153041}.
Digits of k appear first in the 5th powers {32, 243, 16807, 32768, 418195493, 2706784157}.
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Select[Range[10^3],ContainsNone[IntegerDigits[#],Union[IntegerDigits[#^2],IntegerDigits[#^3],IntegerDigits[#^4]]]&] (* James C. McMahon, Jan 17 2024 *)
A253602
Numbers n such that the smallest exponent k for n and n^k to have common digits is 4.
Original entry on oeis.org
22, 47, 92, 157, 187, 188, 192, 552, 558, 577, 707, 772, 922, 2522, 8338, 17177, 66888, 575757, 929522, 1717177, 8888588
Offset: 1
22^2=484 and 22^3=10648 have no digits in common with 22, but 22^4=234256 has some, so 22 is in the sequence.
A029791
Squares k such that digits of sqrt(k) are not present in k or k^(3/2).
Original entry on oeis.org
4, 9, 49, 64, 484, 2209, 2809, 5929, 8464, 24649, 34969, 35344, 36864, 304704, 311364, 332929, 499849, 595984, 850084, 6360484, 69522244, 295049329, 4474004544, 331496123049, 864011148484, 2948696849329, 79006996633744
Offset: 1
A029792
Cubes k such that digits of cube root of k are not present in k^(2/3) or k.
Original entry on oeis.org
8, 27, 343, 512, 10648, 103823, 148877, 456533, 778688, 3869893, 6539203, 6644672, 7077888, 168196608, 173741112, 192100033, 353393243, 460099648, 783777448, 16041140648, 579676470472, 5068062324233, 299257215939072
Offset: 1
A030090
Primes p such that digits of p do not appear in p^2 or p^3 (probably finite).
Original entry on oeis.org
2, 3, 7, 47, 53, 157, 577
Offset: 1
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Select[Prime[Range[1000000]],Intersection[Union[Flatten[ IntegerDigits/@ {#^2,#^3}]],IntegerDigits[#]] == {}&] (* Harvey P. Dale, Apr 25 2018 *)
Showing 1-5 of 5 results.
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