A029800 -id:A029800 - cp's OEIS frontend

A029797 Numbers k such that k^2 and k^3 have the same set of digits.

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

Patrick De Geest

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

			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

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A029793, A029795, A029800, A062397.

Cf. A011557 (a subsequence).

[ n: n in [0..34*10^4] | Set(Intseq(n^2)) eq Set(Intseq(n^3)) ];  // Bruno Berselli, Jun 28 2011

isA029797(n)=Set(Vec(Str(n^2)))==Set(Vec(Str(n^3))) \\ Charles R Greathouse IV, Jun 28 2011

A029801 Squares k such that sqrt(k), k and k^(3/2) all have the same digits.

Original entry on oeis.org

0, 1, 100, 10000, 1000000, 100000000, 10000000000, 1000000000000, 17245415617600, 96929164158121, 100000000000000, 105134200729009, 107276273345476, 107843987961616, 120392793693225, 157426531462729

Offset: 1

Patrick De Geest

Cf. A029800, A029802.

a(n) = A029800(n)^2. - Michel Marcus, Nov 13 2023

A029802 Cubes k such that k^(1/3), k^(2/3) and k all have the same digits.

Original entry on oeis.org

0, 1, 1000, 1000000, 1000000000, 1000000000000, 1000000000000000, 1000000000000000000, 71616072160144576000, 954292919648546514581, 1000000000000000000000, 1077993211772291594473

Offset: 1

Patrick De Geest

Cf. A029800, A029801.

a(n) = A029800(n)^3. - Michel Marcus, Nov 13 2023

A168070 Numbers n with property that n, n^2, n^3, and n^4 have the same set of digits (not counting repetitions).

Original entry on oeis.org

0, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 71624305, 100000000, 103849576, 105823694, 106597243, 108326947, 120463578, 124093657, 126509743, 129306745, 129738560, 139784256, 140786329, 147863502, 148936025, 150973624

Offset: 1

Zak Seidov, Nov 18 2009

If n is here then also 10*n is. But not vice versa: if the term n is multiple of 10 then not necessarily n/10 is the term; e.g., 129738560, 172836950, 175438290 are terms but 12973856, 17283695, 17543829 not.

Lars Blomberg, Table of n, a(n) for n = 1..10000

Cf. A029800.

isok(n) = s1 = Set(digits(n)); (s1 == Set(digits(n^2))) && (s1 == Set(digits(n^3))) && (s1 == Set(digits(n^4))); \\ Michel Marcus, Oct 15 2013

A030093 Primes p such that p, p^2 and p^3 all have the same set of digits.

Original entry on oeis.org

10253497, 74058619, 74563219, 93689027, 102438967, 103259867, 103271569, 104369581, 106725389, 106948327, 107086249, 125384957, 125987473, 127035269, 130256479, 130284769, 136052897, 146970823, 147502963

Offset: 1

Patrick De Geest

Intersection of A029800 and A000040.

sdQ[n_]:=Module[{c=Union/@(IntegerDigits/@{n,n^2,n^3})}, c[[1]] == c[[2]] == c[[3]]]; Select[Prime[Range[8400000]],sdQ] (* Harvey P. Dale, Jan 10 2012 *)

Offset changed by Andrew Howroyd, Aug 11 2024

cp's OEIS Frontend

A029797 Numbers k such that k^2 and k^3 have the same set of digits.

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A029801 Squares k such that sqrt(k), k and k^(3/2) all have the same digits.

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A029802 Cubes k such that k^(1/3), k^(2/3) and k all have the same digits.

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Keywords

Crossrefs

Formula

A168070 Numbers n with property that n, n^2, n^3, and n^4 have the same set of digits (not counting repetitions).

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PARI

A030093 Primes p such that p, p^2 and p^3 all have the same set of digits.

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