A119735 -id:A119735 - cp's OEIS frontend

A124628 Numbers n such that n^3 is zeroless pandigital.

1903, 2257, 2589, 2691, 2842, 2866, 3024, 3159, 3166, 3195, 3598, 3658, 3793, 3908, 4335, 4874, 5032, 5224, 5503, 5596, 5703, 5812, 6009, 6023, 6259, 6289, 6437, 6486, 6645, 7446, 7497, 7592, 7821, 7846, 7899, 8056, 8066, 8166, 8168, 8662, 8677, 8873

Offset: 1

Tanya Khovanova, Dec 21 2006

			1903^3 = 6891541327 (contains all the digits 1 through 9 and doesn't contain 0).

Cf. A119735 Numbers n such that every digit occurs at least once in n^3.

Select[Range[10000], Union[IntegerDigits[ #^3]] == {1, 2, 3, 4, 5, 6, 7, 8, 9} &]

A124629 Primes p such that their cubes are pandigital.

Original entry on oeis.org

5437, 6221, 7219, 8443, 10903, 11353, 15937, 17123, 18229, 19429, 20353, 20903, 20929, 21803, 21841, 21961, 22123, 22283, 22993, 23053, 23369, 23663, 24733, 25183, 25219, 25463, 26317, 26387, 26449, 27127, 27481, 28181, 28631, 28711

Offset: 1

Tanya Khovanova, Dec 21 2006

5437^3 = 160722988453, contains all the digits 0 through 9.

Harvey P. Dale, Table of n, a(n) for n = 1..5000

Cf. Prime subsequence of A119735 - Numbers n such that every digit occurs at least once in n^3.

Select[Range[30000], PrimeQ[ # ] && Union[IntegerDigits[ #^3]] == {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} &]
Select[Prime[Range[4000]],Min[DigitCount[#^3]]>0&] (* Harvey P. Dale, Aug 05 2014 *)

A363909 Numbers whose square and cube taken together contain each decimal digit at least twice.

Original entry on oeis.org

6534, 11027, 11994, 21906, 22178, 22195, 23317, 24567, 27019, 27963, 28354, 29099, 29309, 29339, 29375, 29558, 29621, 30184, 30552, 30584, 31578, 31727, 32447, 32633, 32793, 32912, 32923, 33087, 33257, 33527, 34284, 35717, 36943, 36958, 37697, 38463

Offset: 1

M. F. Hasler, Jun 27 2023

The first term, a(1) = 6534 is the only number of which the square and cube taken together contain each digit 0 to 9 exactly twice.

Presumably a(n) ~ A363905(n) ~ n. - Charles R Greathouse IV, Jul 03 2023

			6534^2 = 42693156, 6534^3 = 278957081304, which together contain each digit 0-9 exactly twice.

Harold Suarez, Interesting..., Number Theory group on LinkedIn, (capture of the original post), June 2023

Cf. A363905: square and cube together contain each digit at least once.
Cf. A036744, A054038, A071519 and A156977 for "pandigital" squares.
Cf. A119735: Numbers n such that every digit occurs at least once in n^3.

is(n)=#Set(n=concat(digits(n^2),digits(n^3)))>9&&(n=vecsort(n))[#n-1]==9&&!n[2]&&!for(i=3,#n-2,n[i]>n[i-1]&&n[i]

cp's OEIS Frontend

A124628 Numbers n such that n^3 is zeroless pandigital.

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A124629 Primes p such that their cubes are pandigital.

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Mathematica

A363909 Numbers whose square and cube taken together contain each decimal digit at least twice.

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