cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

Robert G. Wilson v, Jun 23 2001

Keywords

Comments

Note that 684917 (whose cube is 321302302131323213) so far is the only entry not of the form 10^x + 1.

Crossrefs

Programs

  • Mathematica
    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 *)
  • Python
    A031997_list = [n for n in range(1,10**6,2) if max(str(n**3)) <= '3'] # Chai Wah Wu, Feb 23 2016

Extensions

Term 0 removed and a(12)-a(17) added by Chai Wah Wu, Feb 25 2016
a(18)-a(20) from Giovanni Resta, Mar 14 2020

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

Views

Author

Daniel Blam, Nov 19 2021

Keywords

Comments

This sequence is infinite, because if m > 0 is a term, 1000*m will also be a term.

Crossrefs

Subsequence of A000578 and A043681.

Programs

  • Mathematica
    Select[Range[0, 110000]^3, AllTrue[IntegerDigits[#], MemberQ[{0, 1, 3}, #1] &] &] (* Amiram Eldar, Nov 19 2021 *)
  • Python
    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

Views

Author

Robert G. Wilson v, Jun 23 2001

Keywords

Comments

No more terms through 10^13. - Jon E. Schoenfield, Jul 03 2010
No more terms through 5*10^16. - David A. Corneth, Mar 17 2019

Crossrefs

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).

Programs

  • Mathematica
    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

Views

Author

Colin Barker, Dec 26 2013

Keywords

Comments

It seems that the numbers contain only the digits 0 and 1, and that the reversed fourth power and the square root of the reversed fourth power are both palindromes.
If the above comment is correct, and also if (as it appears) no more than two ones are among the digits of any term, this Mathematica program quickly generates the terms of the sequence: Flatten[Table[Select[ FromDigits/@Permutations[PadRight[PadRight[{},k,1],8,0]],IntegerQ[ Sqrt[ IntegerReverse[#^4]]]&],{k,0,2}]]//Sort - Harvey P. Dale, May 05 2020

Examples

			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.
		

Crossrefs

Programs

  • Magma
    [n: n in [0..10^7] | IsSquare(Seqint(Reverse(Intseq(n^4))))]; // Bruno Berselli, Dec 27 2013
    
  • Mathematica
    Select[Range[0,10^7],IntegerQ[Sqrt[IntegerReverse[#^4]]]&] (* Harvey P. Dale, May 05 2020 *)
  • PARI
    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
    
  • Python
    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.