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 1-5 of 5 results.

A050732 Numbers of form 2^k (for values of k see A050723) containing no pair of consecutive equal digits (probably finite).

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 131072, 1048576, 2097152, 4194304, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 17179869184, 34359738368, 68719476736, 137438953472
Offset: 1

Views

Author

Patrick De Geest, Sep 15 1999

Keywords

Examples

			2^18 = 262144 is missing, for example.
		

Crossrefs

Programs

  • Mathematica
    Select[2^Range[0,40],FreeQ[Differences[IntegerDigits[#]],0] &] (* Jayanta Basu, May 31 2013 *)

A052057 Numbers k such that the decimal expansion of 2^k contains no palindromic substring except single digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 29, 37, 54
Offset: 1

Views

Author

Patrick De Geest, Jan 15 2000

Keywords

Comments

Sequence is probably finite. Next term, if it exists, exceeds 1170.
Next term, if it exists, exceeds 50000. - Sean A. Irvine, Oct 18 2021

Examples

			Record number is 2^54 = 18014398509481984.
		

Crossrefs

Programs

Extensions

Edited by Jon E. Schoenfield, Oct 17 2019

A050725 Decimal expansion of 4^n contains no pair of consecutive equal digits (probably finite).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 14, 15, 16, 17, 18, 24, 27, 28, 33, 34, 40, 52, 63
Offset: 1

Views

Author

Patrick De Geest, Sep 15 1999

Keywords

Comments

No additional terms up to 1200. - Harvey P. Dale, Mar 30 2011
No additional terms up to 100000. - Michel Marcus, Oct 16 2019
Half of even terms of A050723. - Joerg Arndt, Oct 16 2019

Examples

			4^63 = 85070591730234615865843651857942052864.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[0,70],FreeQ[Differences[IntegerDigits[4^#]],0]&] (* Harvey P. Dale, Jul 25 2013 *)
  • PARI
    isok(n) = {my(d = digits(4^n), c = d[1]); for (i=2, #d, if (d[i] == c, return (0)); c = d[i];); return (1);} \\ Michel Marcus, Oct 16 2019

A171550 Numbers n with property that decimal expansion of 2^n+3^n contains no pair of neighbor equal digits (probably finite).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 22, 23, 26, 27, 29, 45, 52, 73
Offset: 0

Views

Author

Zak Seidov, Dec 11 2009

Keywords

Examples

			2^73+3^73 = 67585198634826967968486182914745315.
		

Crossrefs

Cf. A050723 (2^n), A050724 (3^n), A171551 (3^n-2^n).

Programs

  • Mathematica
    Reap[Do[id=IntegerDigits[2^m+3^m];rm=Rest[id]-Most[id];If[FreeQ[rm,0],Sow[m]],{m,0,10000}]][[2,1]]
    Select[Range[0,80],FreeQ[Differences[IntegerDigits[2^#+3^#]],0]&] (* Harvey P. Dale, Dec 09 2021 *)

A171551 Numbers n with property that decimal expansion of 3^n-2^n contains no pair of neighbor equal digits (probably finite).

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 8, 9, 10, 12, 13, 15, 18, 20, 21, 22, 23, 24, 26, 27, 29, 37, 50
Offset: 0

Views

Author

Zak Seidov, Dec 11 2009

Keywords

Examples

			50 is a term because 3^50-2^50 = 717897986565952681927625,
while 49 is not because 3^49-2^49 = 2392(99)328(66)7(66)7576168(77)1 (four pairs of neighbor equal digits).
		

Crossrefs

Cf. A050723 (2^n), A050724 (3^n), A171550 (3^n+2^n).

Programs

  • Mathematica
    Reap[Do[id=IntegerDigits[3^m-2^m];rm=Rest[id]-Most[id];If[FreeQ[rm,0],Sow[m]],{m,0,10000}]][[2,1]]
Showing 1-5 of 5 results.