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

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

Author

M. F. Hasler, Jun 27 2023

Keywords

• nonn
• base
• less

Comments

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

Examples

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

Links

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

Crossrefs

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.

Programs

PARI

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]