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.

A030175 When squared gives number composed of digits {1,2,3}.

Original entry on oeis.org

1, 11, 111, 36361, 363639, 461761, 3636361, 34815389, 362397739, 176412364139, 57637950363639, 3497458093147239, 56843832676142723489, 557963558954625926861
Offset: 1

Views

Author

Patrick De Geest

Keywords

Links

Crossrefs

Cf. A030174; A000290.
Cf. A006716 = A027675^2, A030176 = A030177^2, A058411^2 = A058412, ..., A058473^2 = A058474.
Cf. A136808, A136809, ..., A137147: n and n^2 have digits {...}.
Cf. A277959^2 = A277946 and A277960^2 = A277947: squares whose largest digit is 2 resp. 3.

Programs

  • Mathematica
    Do[ If[ Union[ Join[{1, 2, 3}, IntegerDigits[n^2] ] ] == {1, 2, 3}, Print[n] ], {n, 0, 10^9}]
  • PARI
    lista(nn) = for(n=1, nn, if(setminus(vecsort(digits(n^2), , 8), [1, 2, 3])==[], print1(n, ", "))) \\ Iain Fox, Nov 16 2017

Formula

a(n)^2 = A030174(n). - M. F. Hasler, Nov 16 2017

Extensions

More terms from Patrick De Geest, Mar 01 2000
More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 14 2005
Offset corrected by Iain Fox, Nov 16 2017

A119097 Triangular numbers composed of digits {1,2,3}.

Original entry on oeis.org

1, 3, 21, 231, 2211, 3321, 21321, 32131, 222111, 232221, 11132121, 22221111, 22321221, 2222211111, 2223211221, 12221332311, 222222111111, 222232111221, 1121113113121, 1231322213121, 22222221111111, 22222321111221, 2222222211111111, 2222223211111221
Offset: 1

Views

Author

Giovanni Resta, May 10 2006

Keywords

Links

Crossrefs

Cf. A000217, A030174, A119098. See A119033 for a table of cross-references.

Programs

  • Mathematica
    Flatten[Table[Select[FromDigits/@Tuples[{1,2,3},n],IntegerQ[(Sqrt[ 8#+1]- 1)/2]&],{n,14}]] (* Harvey P. Dale, May 16 2014 *)

Formula

a(n) = A000217(A119098(n)). - Tyler Busby, Mar 31 2023

Extensions

a(23)-a(24) from Tyler Busby, Mar 23 2023

A136812 Numbers k such that k and k^2 use only the digits 0, 1, 2, 3 and 6.

Original entry on oeis.org

0, 1, 6, 10, 11, 60, 100, 101, 106, 110, 111, 361, 600, 601, 1000, 1001, 1006, 1010, 1011, 1060, 1100, 1101, 1106, 1110, 1631, 3606, 3610, 6000, 6001, 6010, 6011, 10000, 10001, 10006, 10010, 10011, 10060, 10100, 10101, 10106, 10110, 10111, 10301, 10306, 10600, 11000, 11001, 11006, 11010, 11060, 11100, 11101, 16310, 32111, 36060, 36100, 36361
Offset: 1

Views

Author

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

Keywords

Comments

Generated with DrScheme.

Examples

			1031316261^2 = 1063613230203020121.

Links

Crossrefs

Cf. A136808, ..., A137147.
Cf. A006716 = A027675^2, A030174 = A030175^2, A030176 = A030177^2, A058411^2 = A058412, ..., A058473^2 = A058474.

A331543 Squares using only decimal digits 0,1,2,3.

Original entry on oeis.org

0, 1, 100, 121, 10000, 10201, 12100, 12321, 22201, 123201, 130321, 1000000, 1002001, 1020100, 1022121, 1210000, 1212201, 1232100, 1320201, 2220100, 3101121, 12320100, 13032100, 100000000, 100020001, 100200100, 100220121, 102010000, 102030201, 102212100, 102232321, 103002201, 121000000, 121022001, 121220100
Offset: 1

Views

Author

Robert Israel, Jan 19 2020

Keywords

Comments

If n is a member then so is 100*n.
All terms == 0, 1, 100, 121, 201 or 321 (mod 1000).

Examples

			a(3) = 100 is a member because 100 = 10^2 and 100 has no digits > 3.

Links

Crossrefs

Cf. A030174.

Programs

  • Maple
    Res:= NULL: count:= 0:
for k from 0 while count < 50 do
  for j in [0,1,100,121,201,321] do
    L:= convert(k,base,4);
    x:= add(L[i]*10^(i-1),i=1..nops(L))*1000+j;
    if issqr(x) then count:= count+1; Res:= Res, x fi
od od:
Res;
Showing 1-4 of 4 results.

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