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

1,1

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

Links

Table of n, a(n) for n=1..36.

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

Example

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

Prog

(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]<n[i+1]&&return)
select(is, [2111..39999])

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.

Sequence in context: A034627 A223217 A229391 * A101704 A147872 A253366

Adjacent sequences: A363906 A363907 A363908 * A363910 A363911 A363912

Keyword

nonn,base,less

Author

M. F. Hasler, Jun 27 2023

Status

approved