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A029797
Numbers k such that k^2 and k^3 have the same set of digits.
5
0, 1, 10, 100, 146, 1000, 1203, 1460, 7652, 8077, 8751, 8965, 10000, 10406, 11914, 12030, 12057, 12586, 12768, 12961, 13055, 14202, 14600, 14625, 16221, 19350, 20450, 21539, 22040, 22175, 23682, 24071, 25089, 25201, 25708, 26653, 26981
OFFSET
1,3
COMMENTS
Conjecture: there exists some m and N for which a(n) = m + n for all n >= N. [Charles R Greathouse IV, Jun 28 2011]
This conjecture is false. If the conjecture is true then for some N we would have k is in the sequence if k >= n. But 10^e + 1 (A062397) is not in the sequence for any integer e >= 0. - David A. Corneth, Nov 13 2023
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
146 is in the sequence as 146^2 = 21316 has digits {1, 2, 3, 6} and 146^3 = 3112136 has digits {1, 2, 3, 6} as well. - David A. Corneth, Nov 13 2023
PROG
(Magma) [ n: n in [0..34*10^4] | Set(Intseq(n^2)) eq Set(Intseq(n^3)) ]; // Bruno Berselli, Jun 28 2011
(PARI) isA029797(n)=Set(Vec(Str(n^2)))==Set(Vec(Str(n^3))) \\ Charles R Greathouse IV, Jun 28 2011
CROSSREFS
Cf. A011557 (a subsequence).
Sequence in context: A207585 A208381 A031187 * A367593 A206983 A207841
KEYWORD
nonn,base
STATUS
approved