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A363909
Numbers whose square and cube taken together contain each decimal digit at least twice.
1
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
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
KEYWORD
nonn,base,less
AUTHOR
M. F. Hasler, Jun 27 2023
STATUS
approved