A029793
Numbers k such that k and k^2 have the same set of digits.
Original entry on oeis.org
0, 1, 10, 100, 1000, 4762, 4832, 10000, 10376, 10493, 11205, 12385, 12650, 14829, 22450, 23506, 24605, 26394, 34196, 36215, 47620, 48302, 48320, 49827, 64510, 68474, 71205, 72510, 72576, 74510, 74528, 79286, 79603, 79836, 94583, 94867, 96123, 98376
Offset: 1
{0, 1, 3, 4, 9} = digits of a(10) = 10493 and of 10493^2 = 110103049;
{0, 1, 2, 5, 6} = digits of a(100) = 162025 and of 162025^2 = 26252100625;
{0, 1, 3, 4, 6, 7, 8} = digits of a(1000) = 1764380 and of 1764380^2 = 3113036784400;
{1, 2, 3, 4, 7, 8, 9} = digits of a(10000) = 14872239 and of 14872239^2 = 221183492873121.
-
import Data.List (nub, sort)
a029793 n = a029793_list !! (n-1)
a029793_list = filter (\x -> digs x == digs (x^2)) [0..]
where digs = sort . nub . show
-- Reinhard Zumkeller, Jun 27 2011
-
[ n: n in [0..10^5] | Set(Intseq(n)) eq Set(Intseq(n^2)) ]; // Bruno Berselli, Jun 28 2011
-
seq(`if`(convert(convert(n,base,10),set) = convert(convert(n^2,base,10),set), n, NULL), n=0..100000); # Nathaniel Johnston, Jun 28 2011
-
digitSet[n_] := Union[IntegerDigits[n]]; Select[Range[0, 99000], digitSet[#] == digitSet[#^2] &] (* Jayanta Basu, Jun 02 2013 *)
-
isA029793(n)=Set(Vec(Str(n)))==Set(Vec(Str(n^2))) \\ Charles R Greathouse IV, Jun 28 2011
-
(0L to 99999L).filter(n => n.toString.toCharArray.toSet == (n * n).toString.toCharArray.toSet) // Alonso del Arte, Jan 19 2020
A029795
Numbers k such that k and k^3 have the same set of digits.
Original entry on oeis.org
0, 1, 10, 100, 1000, 10000, 100000, 107624, 109573, 132485, 138624, 159406, 165640, 192574, 205738, 215806, 251894, 281536, 318725, 419375, 427863, 568314, 642510, 713960, 953867, 954086, 963218, 965760, 1000000, 1008529, 1023479
Offset: 1
109573^3 = 1315559990715517. Since both numbers use the digits 0, 1, 3, 5, 7, 9, and no others, 109573 is in the sequence.
-
[ n: n in [0..8*10^6] | Set(Intseq(n)) eq Set(Intseq(n^3)) ]; // Bruno Berselli, Jun 28 2011
-
seq(`if`(convert(convert(n, base, 10), set) = convert(convert(n^3, base, 10), set), n, NULL), n=0..500000); # Nathaniel Johnston, Jun 28 2011
-
Select[Range[0, 199999], Union[IntegerDigits[#]] == Union[IntegerDigits[#^3]] &] (* Alonso del Arte, Jan 12 2020 *)
-
isA029795(n)=Set(Vec(Str(n)))==Set(Vec(Str(n^3))) \\ Charles R Greathouse IV, Jun 28 2011
A232662
Numbers n such that n and n^7 have the same set of digits.
Original entry on oeis.org
0, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 12635940, 26875130, 29851046, 31572460, 36082794, 38625410, 39756810, 42675139, 47025831, 50748936, 58291760, 65279801, 68249735, 76942451, 78952160, 80572614, 100000000, 102359784, 102374865
Offset: 1
{0, 1, 2, 3, 4, 5, 6, 9} - the set of digits of 12635940 and of 12635940^7, so 12635940 is in the sequence.
-
for(n=0, 102374865, if(Set(Vec(Str(n)))==Set(Vec(Str(n^7))), print1(n, ", ")));
A232660
Numbers n such that n and n^5 have the same set of digits.
Original entry on oeis.org
0, 1, 10, 100, 1000, 10000, 39568, 100000, 395680, 1000000, 2114325, 2751490, 3246105, 3956800, 4356891, 4768209, 4926051, 6274019, 8021439, 10000000, 10267394, 10352849, 10368279, 10456932, 10478632, 10489723, 10489725, 10527934, 10567293, 10639428, 10827439
Offset: 1
{3, 5, 6, 8, 9} - the set of digits of 39568 and of 39568^5, so 39568 is in the sequence.
-
[n : n in [0..10827439] | Set(Intseq(n)) eq Set(Intseq(n^5))];
-
for(n=0, 10827439, if(Set(Vec(Str(n)))==Set(Vec(Str(n^5))), print1(n, ", ")));
A232661
Numbers n such that n and n^6 have the same set of digits.
Original entry on oeis.org
0, 1, 10, 100, 1000, 10000, 100000, 1000000, 1380796, 10000000, 10423786, 10489362, 10532689, 10689247, 10743958, 12645980, 13042697, 13674925, 13807960, 14205893, 14857690, 16892043, 17284360, 17983256, 19046537, 19754203, 20634971, 20637451, 21865409
Offset: 1
{0, 1, 3, 6, 7, 8, 9} - the set of digits of 1380796 and of 1380796^6, so 1380796 is in the sequence.
-
for(n=0, 21865409, if(Set(Vec(Str(n)))==Set(Vec(Str(n^6))), print1(n, ", ")));
A232712
Least positive k (not a power of 10) such that k and k^n have the same set of digits.
Original entry on oeis.org
2, 4762, 107624, 35641, 39568, 1380796, 12635940, 40837596, 102349857, 102567384, 106342987, 129046873, 107623945, 231940678, 239607415, 368709154, 1023456789, 164758903, 176384592, 1023456789, 1023456789, 1023456789, 1023456789, 1023456789, 1023456789
Offset: 1
-
for(n=1, 6, k=1; until(Set(Vec(Str(k)))==Set(Vec(Str(k^n)))&&!(sumdigits(k)==1), k++); print1(k, ", "));
Showing 1-6 of 6 results.
Comments