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 1-2 of 2 results.

A136985 Numbers k such that k and k^2 use only the digits 1, 2, 3 and 9.

Original entry on oeis.org

1, 3, 11, 111, 139
Offset: 1

Views

Author

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

Keywords

Comments

Generated with DrScheme.
No additional terms < 10^11. - Harvey P. Dale, Oct 21 2019
From David A. Corneth, Oct 21 2019: (Start)
No additional terms < 10^31.
The final digits of 1^2, 2^2, 3^2 and 9^2 are 1, 4, 9 and 1 respectively, of which only 1 and 9 are allowed. So a term must end in 1, 3 or 9.
Checking two digits, we see that only numbers ending in 11, 23, 39 or 99 squared have the last two digits allowed.
Similar for three digits, a term must end in one of 111, 911, 123, 323, 923, 139, 239, 339 or 999.
We can recursively see how a number must end and hence reduce the numbers that must be checked. For example, we only have to check 4204352 31-digit numbers to know there are no 31-digit terms.
(End)
No additional terms < 10^38. - Michael S. Branicky, Jul 05 2021

Examples

			139^2 = 19321.

Links

Crossrefs

Cf. A077439, A136809, A136813, A137028, A137105, A137144, A137147.

Programs

  • Mathematica
    With[{c={1,2,3,9}},Select[Flatten[Table[FromDigits/@Tuples[c,n],{n,3}]],SubsetQ[ c,IntegerDigits[#^2]]&]] (* Harvey P. Dale, Oct 21 2019 *)
  • PARI
    \\ See Corneth link. David A. Corneth, Oct 21 2019

A137144 Numbers k such that k and k^2 use only the digits 4, 6, 7 and 8.

Original entry on oeis.org

8, 88, 8874, 68474, 86478
Offset: 1

Views

Author

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

Keywords

Comments

Generated with DrScheme.
No further terms up to and including 1000000. - Harvey P. Dale, Dec 03 2010
No further terms <= 10^40. - Michael S. Branicky, Feb 12 2024
From Pontus von Brömssen, May 01 2024: (Start)
a(6) > 6*10^46 (if it exists).
If k = x*10^m is a term where 1 < x < 10 and k is not 88 or 8874, then 20/3 < x < 8.7674847468864688448864887688468686674647846475.
(End)

Examples

			86478^2 = 7478444484.

Links

Crossrefs

Cf. A077439, A136809, A136813, A136985, A137028, A137105, A137147.

Programs

  • Mathematica
    clearQ[n_]:=Module[{dc=DigitCount[n]},dc[[1]]==dc[[2]]==dc[[3]]==dc[[5]]==dc[[9]]==dc[[10]]==0]
Select[Range[1000000],clearQ[#]&&clearQ[#^2]&] (* Harvey P. Dale, Dec 03 2010 *)
Showing 1-2 of 2 results.

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

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