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.

A099970 Write 1/e as a binary fraction; read this from left to right and whenever a 1 appears, note the integer formed by reading leftwards from that 1. Then convert those integers from binary into decimal numbers.

Original entry on oeis.org

1, 5, 13, 29, 61, 573, 2621, 6717, 23101, 88637, 350781, 875069, 9263677, 26040893, 93149757, 227367485, 2374851133, 10964785725, 28144654909, 165583608381, 440461515325, 990217329213, 3189240584765, 7587287095869, 16383380118077
Offset: 0

Views

Author

N. J. A. Sloane, Nov 13 2004, based on correspondence from Artur Jasinski, Mar 25 2003

Keywords

Examples

			1/e = 0.367879441171442321595523770161460867445811131031767834507... = 0.010111100010110101011000110110001011001110111100110111110001101010111010110111 in binary.
		

Crossrefs

Programs

  • Mathematica
    d = 100; l = First[RealDigits[N[1/E, d], 2]]; Do[m = Take[l, n]; k = Length[m]; If[m[[k]] == 1, Print[FromDigits[Reverse[m], 2]]], {n, 1, d}] (* Ryan Propper, Aug 18 2005 *)
    Module[{nn=50,e},e=RealDigits[1/E,2, 50][[1]];Table[If[e[[n]]== 0, Nothing,FromDigits[ Reverse[Take[e,n]],2]],{n,nn}]] (* Harvey P. Dale, Sep 17 2020 *)

Formula

a(n) = A099969(n)/2. - Michel Marcus, Nov 03 2013

Extensions

More terms from Ryan Propper, Aug 18 2005
Definition amended by Harvey P. Dale, Sep 17 2020

A099969 Write 1/e as a binary fraction; read this from left to right and whenever a 1 appears, note the integer formed by reading leftwards from that 1.

Original entry on oeis.org

2, 10, 26, 58, 122, 1146, 5242, 13434, 46202, 177274, 701562, 1750138, 18527354, 52081786, 186299514, 454734970, 4749702266, 21929571450, 56289309818, 331167216762, 880923030650, 1980434658426, 6378481169530, 15174574191738
Offset: 0

Views

Author

N. J. A. Sloane, Nov 13 2004, based on correspondence from Artur Jasinski, Mar 25 2003

Keywords

Examples

			1/e = 0.367879441171442321595523770161460867445811131031767834507... = 0.010111100010110101011000110110001011001110111100110111110001101010111010110111 in binary.
From the binary expansion we get 10 = 2, 1010 = 10, 11010 = 26, 111010 = 58, 1111010 = 122, etc.
		

Crossrefs

Programs

  • Mathematica
    d = 100; l = First[RealDigits[N[1/E, d], 2]]; Do[m = Take[l, n]; k = Length[m]; If[m[[k]] == 1, Print[2*FromDigits[Reverse[m], 2]]], {n, 1, d}] (* Ryan Propper, Aug 18 2005 *)

Extensions

More terms from Ryan Propper, Aug 18 2005

A099971 Write (sqrt(5)-1)/2 as a binary fraction; read this from left to right and whenever a 1 appears, note the integer formed by reading leftwards from that 1.

Original entry on oeis.org

1, 9, 25, 57, 121, 1145, 3193, 11385, 27769, 60537, 191609, 453753, 978041, 2026617, 10415225, 27192441, 94301305, 228519033, 496954489, 2644438137, 11234372729, 28414241913, 62773980281, 131493457017, 268932410489, 543810317433
Offset: 0

Views

Author

N. J. A. Sloane, Nov 13 2004, based on correspondence from Artur Jasinski, Mar 25 2003

Keywords

Examples

			(sqrt(5)-1)/2 = 0.618033988749894848204586834365638117720309179805762862135... = 0.100111100011011101111001101110010111111101001010011111000001010111110011... in binary.
		

Crossrefs

Programs

  • Mathematica
    d = 100; l = First[RealDigits[N[(Sqrt[5]-1)/2, d], 2]]; Do[m = Take[l, n]; k = Length[m]; If[m[[k]] == 1, Print[FromDigits[Reverse[m], 2]]], {n, 1, d}] (* Ryan Propper, Aug 18 2005 *)

Extensions

More terms from Ryan Propper, Aug 18 2005

A099972 Write 1/sqrt(2) as a binary fraction; read this from left to right and whenever a 1 appears, note the integer formed by reading leftwards from that 1.

Original entry on oeis.org

1, 5, 13, 45, 173, 8365, 73901, 204973, 467117, 991405, 5185709, 13574317, 80683181, 214900909, 1288642733, 3436126381, 7731093677, 16321028269, 33500897453, 67860635821, 136580112557, 686335926445, 1785847554221
Offset: 0

Views

Author

N. J. A. Sloane, Nov 13 2004, based on correspondence from Artur Jasinski, Mar 25 2003

Keywords

Examples

			1/sqrt(2) = 0.7071067811865475244008443621048490392848359376885... = 0.10110101000001001111001100110011111110011101111001100100100001000101100101111101100010011011 in binary.
		

Crossrefs

Programs

  • Mathematica
    d = 100; l = First[RealDigits[N[1/Sqrt[2], d], 2]]; Do[m = Take[l, n]; k = Length[m]; If[m[[k]] == 1, Print[FromDigits[Reverse[m], 2]]], {n, 1, d}] (* Ryan Propper, Aug 18 2005 *)
    Module[{rd=RealDigits[1/Sqrt[2],2,50][[1]],pos},pos=Flatten[Position[rd,1]];Table[ FromDigits[ Reverse[Take[rd,n]],2],{n,pos}]] (* Harvey P. Dale, Jul 29 2013 *)

Extensions

More terms from Ryan Propper, Aug 18 2005

A099974 Write log(2) as a binary fraction; read this from left to right and whenever a 1 appears, note the integer formed by reading leftwards from that 1.

Original entry on oeis.org

1, 5, 13, 141, 653, 1677, 3725, 20109, 544397, 2641549, 6835853, 15224461, 32001677, 65556109, 132664973, 266882701, 803753613, 1877495437, 4024979085, 8319946381, 16909880973, 51269619341, 601025433229, 1700537061005
Offset: 0

Views

Author

N. J. A. Sloane, Nov 13 2004, based on correspondence from Artur Jasinski, Mar 25 2003

Keywords

Examples

			log(2) = 0.69314718055994530941723212145817656807550013436025525412... = 0.1011000101110010000101111111011111010001110011110111100110101011110010011110... in binary.
		

Crossrefs

Programs

  • Mathematica
    d = 100; l = First[RealDigits[N[Log[2], d], 2]]; Do[m = Take[l, n]; k = Length[m]; If[m[[k]] == 1, Print[FromDigits[Reverse[m], 2]]], {n, 1, d}] (* Ryan Propper, Aug 17 2005 *)
    Module[{nn=50,l2},l2=RealDigits[Log[2],2,nn][[1]];Table[FromDigits[ Reverse[ Take[ l2,n]],2],{n,nn}]]//Union (* Harvey P. Dale, Mar 29 2016 *)

Extensions

More terms from Ryan Propper, Aug 17 2005
Showing 1-5 of 5 results.