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 1-3 of 3 results.

A030287 a(n) is the smallest k > a(n-1) such that k^2 has no digit in common with a(n-1)^2.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 9, 15, 19, 20, 23, 26, 29, 30, 34, 47, 56, 65, 83, 85, 90, 156, 241, 264, 265, 291, 300, 334, 448, 563, 638, 715, 780, 961, 2000, 2261, 2457, 3335, 5478, 7154, 9128, 9569, 14220, 17654, 20000, 22609, 26462, 28604, 30000
Offset: 0

Views

Author

Patrick De Geest

Keywords

Comments

a(n) = sqrt(A030288(n)). - Zak Seidov, Feb 20 2009

Links

Crossrefs

Cf. A030288: squares whose digits do not appear in previous term.
Cf. A067581: a(n) has no digit of a(n-1).
See also A294660.

Programs

  • Mathematica
    Nest[Append[#, Block[{k = Last[#] + 1}, While[IntersectingQ @@ IntegerDigits@ {Last[#]^2, k^2}, k++]; k]] &, {0}, 50] (* Michael De Vlieger, Nov 03 2017 *)
  • PARI
    next_A030287(n,D=Set(digits(n^2)))=for(k=n+1,oo,#setintersect(Set(digits(k^2)),D)||return(k))
print1(a=0);for(i=1,99,print1(","a=next_A030287(a))) \\ M. F. Hasler, Nov 08 2017

Extensions

Edited by N. J. A. Sloane, Feb 22 2009 at the suggestion of R. J. Mathar

A030289 a(n+1) is the next larger cube with no digits in common with a(n), a(0) = 0.

Original entry on oeis.org

0, 1, 8, 27, 64, 125, 343, 512, 4096, 5832, 64000, 91125, 300763, 941192, 3375000, 8489664, 13312053, 86444696669696, 100175333300307, 488224224494488, 510657175657000, 2233398984434344, 5177717000000000, 6393843393228864
Offset: 0

Views

Author

Patrick De Geest

Keywords

Comments

From a(24) on, even-indexed terms are powers of 1000, odd-indexed terms are the next larger cube to a(n-1)*20/9 with no digit 0 or 1, cf. A030290. - M. F. Hasler, Nov 12 2017

Links

Crossrefs

Squares whose digits do not appear in previous term: A030288.
Primes whose digits do not appear in previous term: A030284.
Cf. A030290: cube roots of the terms.

Programs

  • Mathematica
    bb={0}; idi1=IntegerDigits[0]; Do[idi=IntegerDigits[r=i^3]; If[Intersection[idi, idi1]=={}, bb={bb, r}; idi1=idi], {i, 1, 100000}]; fla=Flatten[bb] (* Zak Seidov, Feb 17 2005 *)
Nest[Append[#, Block[{k = Last@ # + 1, m = IntegerDigits[Last[#]^3]}, While[IntersectingQ[IntegerDigits[k^3], m], k++]; k]] &, {0}, 23]^3 (* Michael De Vlieger, Nov 13 2017 *)
  • PARI
    next_A030289(n,D(n)=Set(digits(n)),S=D(n))={if(n>6e15,S[1]&&return(1000^(logint(n,1000)+1));n=n*20\9); for(k=sqrtnint(n,3)+1,oo,#setintersect(D(k^3),S)||return(k^3))} \\ M. F. Hasler, Nov 12 2017

Formula

a(n) = A030290(n)^3. - David W. Wilson, Nov 08 2017

A100373 Lexicographically earliest increasing sequence of composite numbers such that the digits of a(n) do not appear in a(n-1).

Original entry on oeis.org

4, 6, 8, 9, 10, 22, 30, 42, 50, 62, 70, 81, 90, 111, 200, 314, 500, 611, 700, 812, 900, 1111, 2000, 3111, 4000, 5111, 6000, 7111, 8000, 9111, 20000, 31111, 40000, 51111, 60000, 71111, 80000, 91111, 200000, 311113, 400000, 511112, 600000, 711111
Offset: 1

Views

Author

Labos Elemer, Dec 01 2004

Keywords

Links

Crossrefs

Cf. A002808, A030283, A030284, A030285, A030286, A030287, A030288, A030289, A030290.

Programs

  • Maple
    f:= proc(x) local L,S,carry,m,nL,b,d0,Lz,z,i,d;
  L:= convert(x,base,10);
  nL:= nops(L);
  S:= sort(convert({$0..9} minus convert(L,set),list));
  b:= nops(S);
  d0:= min(select(`>`,S,L[-1]));
  if d0 = infinity then
    if S[1] = 0 then Lz:= Vector([0$nL, S[2]])
    else Lz:= Vector([S[1]$(nL+1)])
    fi
  else
    Lz:= Vector([S[1]$(nL-1),d0])
  fi;
  d:= LinearAlgebra:-Dimension(Lz);
  do
    z:= add(Lz[i]*10^(i-1),i=1..d);
    if not isprime(z) then return z fi;
    carry:= true;
    for i from 1 to d while carry do
      if Lz[i] = S[-1] then Lz[i]:= S[1]
      else
        carry:= false; if member(Lz[i],S,'m') then Lz[i]:= S[m+1] fi
      fi
    od;
    if carry then d:= d+1; if S[1] = 0 then Lz(d):= S[2] else Lz(d) := S[1] fi fi
  od;
end proc:
R:= 4: r:= 4:
for i from 2 to 100 do
  r:= f(r);
  R:= R,r
od:
R; # Robert Israel, Feb 27 2025
  • Mathematica
    ta={1};Do[s1=IntegerDigits[Part[ta, Length[ta]]]; s2=IntegerDigits[n];If[Equal[Intersection[s1, s2], {}] &&!PrimeQ[n], Print[{Last[ta], n}];ta=Append[ta, n]], {n, 1, 1000000}];ta=Delete[ta, 1]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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