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
1/e = 0.367879441171442321595523770161460867445811131031767834507... = 0.010111100010110101011000110110001011001110111100110111110001101010111010110111 in binary.
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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 *)
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
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.
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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 *)
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
(sqrt(5)-1)/2 = 0.618033988749894848204586834365638117720309179805762862135... = 0.100111100011011101111001101110010111111101001010011111000001010111110011... in binary.
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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 *)
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
1/sqrt(2) = 0.7071067811865475244008443621048490392848359376885... = 0.10110101000001001111001100110011111110011101111001100100100001000101100101111101100010011011 in binary.
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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 *)
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
log(2) = 0.69314718055994530941723212145817656807550013436025525412... = 0.1011000101110010000101111111011111010001110011110111100110101011110010011110... in binary.
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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 *)
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