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 1-8 of 8 results.

A199340 Primes having only {0, 3, 4} as digits.

Original entry on oeis.org

3, 43, 433, 443, 3343, 3433, 4003, 30403, 33343, 33403, 34033, 34303, 34403, 40343, 40433, 43003, 43403, 300043, 300343, 304033, 304303, 304433, 330433, 333433, 334043, 334333, 334403, 343303, 343333, 343433, 400033, 403003, 403043, 403433, 430303, 430333
Offset: 1

Views

Author

M. F. Hasler, Nov 05 2011

Keywords

Comments

All terms end in '3'. This could be used to speed up the given program.
A020461 is a subsequence. - Vincenzo Librandi, Jul 23 2015

Links

Crossrefs

Cf. Primes that contain only the digits (3,4,k): this sequence (k=0), A199341 (k=1), A199342 (k=2), A199345 (k=5), A199346 (k=6), A199347 (k=7), A199348 (k=8), A199349 (k=9).
Cf. A020449 - A020472, A199325 - A199329.
Cf. A058429, A058430.

Programs

  • Magma
    [p: p in PrimesUpTo(5*10^5) | Set(Intseq(p)) subset [3, 4, 0]]; // Vincenzo Librandi, Jul 23 2015
  • Mathematica
    Select[Prime[Range[5 10^4]], Complement[IntegerDigits[#], {3, 4, 0}]=={} &] (* Vincenzo Librandi, Jul 23 2015 *)
Select[FromDigits/@Tuples[{0,3,4},6],PrimeQ] (* Harvey P. Dale, Mar 21 2020 *)
Select[10#+3&/@FromDigits/@Tuples[{0,3,4},5],PrimeQ] (* Harvey P. Dale, May 02 2022 *)
  • PARI
    a(n, list=0, L=[0, 3, 4], reqpal=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&!L[1]), #L]), isprime(t=vector(d, i, L[v[i]])*u)||next; reqpal && !isprime(A004086(t)) && next; list && print1(t", "); n--||return(t)))} \\ Syntax updated for current PARI version. - M. F. Hasler, Jul 25 2015
  • PARI
    {forprime(p=3,1e6,p%10==3&&!setminus(Set(digits(p)),[3,4])&&print1(p","))} \\ [0] evaluates to false. - M. F. Hasler, Jul 25 2015

A058430 Squares composed of digits {0,3,4}, not ending with zero.

Original entry on oeis.org

4, 300304, 343030433344, 3433000433443344, 40330334403443044, 33330430344333340030340440344044034304, 434003044400343443044430000434430333044043044
Offset: 1

Views

Author

Patrick De Geest, Nov 15 2000

Keywords

Links

Programs

Formula

a(n) = A058429(n)^2. - M. F. Hasler, Aug 29 2012

Extensions

One more term from M. F. Hasler, May 14 2007
One more term from Mishima's page added by Max Alekseyev, Jul 13 2009

A058433 Numbers k such that k^2 contains only digits {0,3,9}, not ending with zero.

Original entry on oeis.org

3, 969071253
Offset: 1

Views

Author

Patrick De Geest, Nov 15 2000

Keywords

Comments

No more terms up to 10^23. - Charles R Greathouse IV, Jul 27 2009

Links

Crossrefs

Cf. A058434 (the squares), A058429 (similar for digits {0,3,4}).

Programs

  • Mathematica
    Sqrt[#]&/@Select[FromDigits/@Tuples[{0,3,9},18],Mod[#,10]!=0&&IntegerQ[Sqrt[#]]&] (* Harvey P. Dale, May 28 2025 *)
  • PARI
    /* helper function: */
admissibleMod(M=10^5, t=[3, 9], debug=0)={ my(p=1, v); while(M > p *= 10,
    t = concat([t, t + t[1]*v=vector(#t, i, p), t + t[2]*v]));
    debug && print("t="t); t=Set(t); v=[];
    for(k=1, M, setsearch(t, k^2 % M) && v=concat(v, k)); concat(v, M+v[1])}
/* optional arguments: Nmax = upper search limit, N = start / lower limit,
   addMod = step/chunk size, debug: 0=silent, 1=verbose */
A058433(Nmax=1e10, N=1, addMod=10^5, debug=1)={ my(a=[], d=1,
  addNext = admissibleMod(addMod=10^logint(addMod\/1, 10), [3, 9]),
  add = vector(addMod, i, i-1 > addNext[d] && d++; addNext[d]-i+1),
  pow10 = [10^k | k<-[0..logint((Nmax \/= 1)^2, 10)]],
  nextOK = [if(n, n*pow10) | n<-[0, 2, 1, 0, 5, 4, 3, 2, 1, 0]]); N \/= 1;
  while( Nmax >= N, my(N2 = N^2, numDigits = logint(N2, 10)+1,
                       place = nextOK[1 + d = N2 \ pow10[numDigits]]);
    if( place, N = max(sqrtint(place[numDigits] + d*pow10[numDigits]), N+1);
               next); place = 1;
    my(Nnext = min(sqrtint((d+1)*pow10[numDigits]), Nmax));
    debug && print("checking from "N" to "Nnext": <= ",
                   1+max(0, Nnext-N)*(#addNext-1)\ addMod," candidates.");
    while( Nnext >= N += add[1 + N % addMod],
      my(dr = divrem( N2 = N^2, pow10[place = numDigits] ));
      while( place-- && !d=nextOK[1+ (dr = divrem(dr[2], pow10[place]))[1]], );
      place || break; N = sqrtint(N2 - dr[2] + d[place]) + 1;
    ); if( !place, debug && print(N "^2 = ", N^2); a=concat(a,N));
    N = Nnext*3\2+1); a} \\ M. F. Hasler, May 14 2007

A136927 Numbers k such that k and k^2 use only the digits 0, 3, 4, 5 and 6.

Original entry on oeis.org

0, 6, 60, 66, 600, 656, 660, 666, 6000, 6560, 6600, 6660, 6666, 60000, 63566, 65600, 66000, 66600, 66660, 66666, 600000, 603656, 604434, 635660, 656000, 660000, 660656, 666000, 666600, 666660, 666666, 6000000, 6036560, 6044340, 6356600, 6560000, 6600000, 6606560, 6660000, 6666000, 6666600, 6666660, 6666666, 60000000, 60054434, 60365600
Offset: 1

Views

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

Comments

Generated with DrScheme.
See also A058429-A058430. - M. F. Hasler, Jan 24 2008

Examples

			665605465350506^2 = 443030635504463643353434456036.

Links

Programs

  • Mathematica
    With[{c={0,3,4,5,6},nn=8},Select[FromDigits/@Tuples[c,nn],SubsetQ[ c,IntegerDigits[ #^2]]&]] (* Harvey P. Dale, Apr 27 2022 *)

A136928 Numbers k such that k and k^2 use only the digits 0, 3, 4, 5 and 8.

Original entry on oeis.org

0, 548, 5480, 54800, 55548, 548000, 555388, 555480, 588048, 5480000, 5553880, 5554548, 5554800, 5834388, 5880480, 54800000, 55538800, 55545480, 55548000, 58343880, 58804800, 548000000, 550500548, 555388000, 555454800, 555480000, 583438800, 588048000, 5480000000, 5505005480, 5553880000, 5554548000, 5554800000, 5834388000
Offset: 1

Views

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

Comments

Generated with DrScheme.

Examples

			583854308054548^2 = 340885853033855033588543484304.

Links

Crossrefs

See also A058429-A058430. - M. F. Hasler, Jan 24 2008

A136929 Numbers k such that k and k^2 use only the digits 0, 3, 4, 5 and 9.

Original entry on oeis.org

0, 3, 30, 300, 3000, 30000, 30503, 30903, 300000, 305030, 309030, 550503, 950503, 953903, 3000000, 3005003, 3009003, 3050300, 3055003, 3090300, 5505030, 9505030, 9539030, 30000000, 30050030, 30090030, 30503000, 30550030, 30903000, 55050300, 95050300, 95055003, 95390300, 300000000, 300050003, 300050503, 300090003, 300500300
Offset: 1

Views

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

Comments

Generated with DrScheme.
See also A058429-A058430. - M. F. Hasler, Jan 24 2008

Examples

			950439335440903^2 = 903334930353345333433405455409.

Links

A136930 Numbers k such that k and k^2 use only the digits 0, 3, 4, 6 and 7.

Original entry on oeis.org

0, 6, 60, 600, 6000, 60000, 66076, 600000, 660760, 6000000, 6607600, 60000000, 60003706, 60036706, 66036076, 66066376, 66076000, 600000000, 600037060, 600306344, 600367060, 600373006, 606336074, 660360760, 660663760, 660760000, 660760474, 6000000000, 6000036706, 6000370600, 6000637006, 6003063440, 6003670600, 6003730060
Offset: 1

Views

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

Comments

Generated with DrScheme.
See also A058429-A058430. - M. F. Hasler, Jan 24 2008

Examples

			660760703770306^2 = 436604707647030077763607333636.

Links

A136931 Numbers k such that k and k^2 use only the digits 0, 3, 4, 6 and 8.

Original entry on oeis.org

0, 6, 8, 60, 80, 600, 800, 6000, 6638, 6808, 6844, 8000, 60000, 60406, 60688, 66380, 66808, 68080, 68440, 80000, 600000, 604060, 606880, 663800, 668080, 680800, 684400, 800000, 6000000, 6003406, 6004006, 6040600, 6068800, 6638000, 6680800, 6808000, 6844000, 8000000, 60000000, 60034060, 60040060, 60406000, 60688000, 66363008, 66380000
Offset: 1

Views

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

Comments

Generated with DrScheme.

Examples

			683084686436344^2 = 466604688843838404646364086336.

Links

Crossrefs

See also A058429-A058430. - M. F. Hasler, Jan 24 2008

Programs

  • Mathematica
    s={0,3,4,6,8}; Select[Range[0,10^6], SubsetQ[s, Sort[DeleteDuplicates[IntegerDigits[#]]]] && SubsetQ[s, Sort[DeleteDuplicates[IntegerDigits[#^2]]]] &] (* Stefano Spezia, Aug 11 2025 *)
Showing 1-8 of 8 results.

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

Content is available under The OEIS End-User License Agreement.