A031997
Odd numbers which when cubed give number composed just of the digits 0, 1, 2, 3.
Original entry on oeis.org
1, 11, 101, 1001, 10001, 100001, 684917, 1000001, 10000001, 100000001, 1000000001, 10000000001, 100000000001, 1000000000001, 10000000000001, 100000000000001, 1000000000000001, 10000000000000001, 100000000000000001, 1000000000000000001
Offset: 1
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Do[ If[ Union[ IntegerDigits[ n^3 ] ] [ [ -1 ] ] < 4, Print[ n ] ], {n, 1, 10^9, 2} ] (* corrected by Friedjof Tellkamp, Apr 24 2025 *)
(* faster code *)
DigitsLEQ3[n_] := And @@ (LessEqual[#, 3] & /@ IntegerDigits[n])
Arr = {1, 7}; For[i = 1, i < 10, i++, Arr = Flatten[Table[Select[Arr + 10^i j, DigitsLEQ3[Mod[#^3, 10^(i+1)]] &], {j, 0, 9}]]];
Select[Arr, DigitsLEQ3[#^3] &] (* Friedjof Tellkamp, Apr 25 2025 *)
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A031997_list = [n for n in range(1,10**6,2) if max(str(n**3)) <= '3'] # Chai Wah Wu, Feb 23 2016
Term 0 removed and a(12)-a(17) added by
Chai Wah Wu, Feb 25 2016
A342975
Cubes composed of digits {0, 1, 3}.
Original entry on oeis.org
0, 1, 1000, 1331, 1000000, 1030301, 1331000, 1000000000, 1003003001, 1030301000, 1331000000, 1000000000000, 1000300030001, 1003003001000, 1030301000000, 1331000000000, 1000000000000000, 1000030000300001, 1000300030001000, 1003003001000000, 1030301000000000, 1331000000000000
Offset: 1
-
Select[Range[0, 110000]^3, AllTrue[IntegerDigits[#], MemberQ[{0, 1, 3}, #1] &] &] (* Amiram Eldar, Nov 19 2021 *)
-
from itertools import islice, count
def A342975(): return filter(lambda n: set(str(n)) <= {'0','1','3'},(n**3 for n in count(0)))
A342975_list = list(islice(A342975(),20)) # Chai Wah Wu, Nov 19 2021
A061809
When cubed gives number composed just of the digits 1, 2, 3, 4.
Original entry on oeis.org
1, 7, 11, 68, 1039247
Offset: 1
Cf.
A031997 (odd and digits 0,1,2,3),
A043681 (0,1,2,3),
A048792 (0,1,2,3,4),
A061813 (1,2,3,4,5).
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Do[ If[ Union[ Join[ {1, 2, 3, 4}, IntegerDigits[n^3] ]] == {1, 2, 3, 4}, Print[n]], {n, 0, 10^8} ]
Table[Surd[#,3]&/@Select[FromDigits/@Tuples[{1,2,3,4},n],IntegerQ[ Surd[ #,3]]&],{n,6}]//Flatten (* The program generates the first 4 terms of the sequence; to generate the 5th term, change the "6" to "19," but the program will take a long time to run. *) (* Harvey P. Dale, Apr 13 2021 *)
A234472
Numbers that when raised to the fourth power and written backwards give squares.
Original entry on oeis.org
0, 1, 10, 11, 100, 101, 110, 1000, 1001, 1010, 1100, 10000, 10001, 10010, 10100, 11000, 100000, 100001, 100010, 100100, 101000, 110000, 1000000, 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 10000000, 10000001, 10000010, 10000100, 10001000, 10010000
Offset: 1
101 is in the sequence because 101^4 = 104060401 and 104060401 = 10201^2.
110 is in the sequence because 110^4 = 146410000 and 14641 = 121^2.
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[n: n in [0..10^7] | IsSquare(Seqint(Reverse(Intseq(n^4))))]; // Bruno Berselli, Dec 27 2013
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Select[Range[0,10^7],IntegerQ[Sqrt[IntegerReverse[#^4]]]&] (* Harvey P. Dale, May 05 2020 *)
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revint(n) = m=n%10; n\=10; while(n>0, m=m*10+n%10; n\=10); m
s=[]; for(i=0, 1000000, if(issquare(revint(i^4)), s=concat(s, i))); s
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from itertools import count, islice
from sympy import integer_nthroot
def A234472_gen(startvalue=0): # generator of terms >= startvalue
return filter(lambda n:integer_nthroot(int(str(n**4)[::-1]),2)[1], count(max(startvalue,0)))
A234472_list = list(islice(A234472_gen(),10)) # Chai Wah Wu, Nov 18 2022
Showing 1-4 of 4 results.
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