A095062 -id:A095062 - cp's OEIS frontend

A095283 Primes whose binary-expansion ends with an odd number of 1's.

5, 7, 13, 17, 23, 29, 31, 37, 41, 53, 61, 71, 73, 89, 97, 101, 103, 109, 113, 127, 137, 149, 151, 157, 167, 173, 181, 193, 197, 199, 223, 229, 233, 241, 257, 263, 269, 277, 281, 293, 311, 313, 317, 337, 349, 353, 359, 373, 383, 389, 397, 401, 409

Offset: 1

Antti Karttunen, Jun 04 2004

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Intersection of A000040 & A079523. Complement of A095282 in A000040. Cf. A027697, A095293.

q:= proc(n) local i, l, r; l, r:= convert(n, base, 2), 0;
      for i to nops(l) while l[i]=1 do r:=r+1 od; is(r, odd)
    end:
select(q, [ithprime(i)$i=1..150])[];  # Alois P. Heinz, Dec 15 2019

Select[Prime[Range[100]], MatchQ[IntegerDigits[#, 2], {b:(1)..}|{_, 0, b:(1)..} /; OddQ[Length[{b}]]]&] (* Jean-François Alcover, Jan 03 2022 *)

is(n)=valuation(n+1,2)%2 && isprime(n) \\ Charles R Greathouse IV, Oct 09 2013

from sympy import isprime
def ok(n): b = bin(n); return (len(b)-len(b.rstrip("1")))%2 and isprime(n)
print([k for k in range(1, 401) if ok(k)]) # Michael S. Branicky, Jan 03 2022

A095284 Primes in whose binary expansion the number of 1 bits is > 5 + number of 0 bits.

Original entry on oeis.org

127, 191, 223, 239, 251, 383, 479, 503, 509, 751, 863, 887, 983, 991, 1013, 1019, 1021, 1279, 1471, 1531, 1663, 1759, 1783, 1787, 1789, 1951, 1979, 1999, 2011, 2027, 2029, 2039, 2543, 2551, 2557, 2687, 2879, 2927, 2939, 2999, 3023, 3037

Offset: 1

Antti Karttunen, Jun 04 2004

A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095285 in A000040. Subset of A095322. Subset: A095312. Cf. also A095286, A095294.

B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
if(b1 > (5+b0), return(1);, return(0););};
forprime(x = 31, 3037, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 12 2011

A095285 Primes in whose binary expansion the number of 1 bits is <= 5 + number of 0 bits.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 211, 227, 229, 233, 241, 257, 263, 269, 271, 277, 281, 283

Offset: 1

Antti Karttunen, Jun 04 2004

Differs from primes (A000040) first time at n=31, where a(31)=131, while A000040(31)=127, as 127 whose binary expansion is 1111111, with 7 1-bits and no 0-bits is the first prime excluded from this sequence. Note that 63 (111111 in binary) is not prime.

A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095284 in A000040. Subset: A095323. Subset of A095313, from which it differs first time at n=42, where a(42)=193 (11000001 in binary) while A095313(42)=191 (10111111 in binary). Cf. also A095286, A095295.

B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
if(b1 <= (5+b0), return(1);, return(0););};
forprime(x = 2, 283, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 12 2011

A095287 Primes in whose binary expansion the number of 1-bits is <= 1 + number of 0-bits.

Original entry on oeis.org

2, 5, 17, 19, 37, 41, 67, 71, 73, 83, 89, 97, 101, 113, 131, 137, 139, 149, 163, 193, 197, 257, 263, 269, 271, 277, 281, 283, 293, 307, 313, 331, 337, 353, 389, 397, 401, 409, 419, 421, 433, 449, 457, 521, 523, 541, 547, 557, 563, 569, 577, 587, 593, 601, 613

Offset: 1

Antti Karttunen, Jun 04 2004

			From _Indranil Ghosh_, Feb 03 2017: (Start)
5 is in the sequence because 5_10 = 101_2. '101' has two 1's and one 0.
17 is in the sequence because 17_10 = 10001_2. '10001' has two 1's and three 0's. (End)

Indranil Ghosh, Table of n, a(n) for n = 1..25000
A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095286 in A000040. Subset: A095075. Subset of A095315. Cf. also A095297.

Select[Prime[Range[200]],DigitCount[#,2,1]<=1+DigitCount[#,2,0]&] (* Harvey P. Dale, Apr 18 2023 *)

forprime(p=2,613,v=binary(p);s=0;for(k=1,#v,s+=if(v[k]==1,+1,-1));if(s<=1,print1(p,", "))) \\ Washington Bomfim, Jan 13 2011

from sympy import isprime
i=1
j=1
while j<=250:
    if isprime(i) and bin(i)[2:].count("1")<=1+bin(i)[2:].count("0"):
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 03 2017

A095312 Primes in whose binary expansion the number of 1-bits is > 6 + number of 0-bits.

Original entry on oeis.org

127, 383, 479, 503, 509, 991, 1019, 1021, 1279, 1471, 1531, 1663, 1759, 1783, 1787, 1789, 1951, 1979, 1999, 2011, 2027, 2029, 2039, 3067, 3581, 3583, 3823, 3967, 4027, 4079, 4091, 4093, 5087, 5119, 5503, 5623, 5879, 6007, 6011, 6047

Offset: 1

Antti Karttunen, Jun 04 2004

Harvey P. Dale, Table of n, a(n) for n = 1..10000
A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095313 in A000040. Subset of A095284. Cf. also A095332.

n1bQ[n_]:=Module[{idn2=IntegerDigits[n,2]},Count[idn2,1]>6+Count[idn2,0]]; Select[Prime[Range[1000]],n1bQ] (* Harvey P. Dale, Jun 25 2014 *)

forprime(p=2,6100,v=binary(p);s=0;for(k=1,#v,s+=if(v[k]==1,+1,-1));if(s>6,print1(p,", "))) \\ Washington Bomfim, Jan 13 2011

A095313 Primes in whose binary expansion the number of 1-bits is <= 6 + number of 0-bits.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269

Offset: 1

Antti Karttunen, Jun 04 2004

Differs from primes (A000040) first time at n=31, where a(31)=131, while A000040(31)=127, as 127 whose binary expansion is 1111111, with 7 1-bits and no 0-bits is the first prime excluded from this sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095312 in A000040. Subset: A095285, from which it differs first time at n=42, where a(42)=191 (10111111 in binary), while A095285(42)=193 (11000001 in binary). Cf. also A095333.

Select[Prime[Range[100]],DigitCount[#,2,1]<= DigitCount[#,2,0]+6&] (* Harvey P. Dale, Aug 18 2016 *)

forprime(p=2,269,v=binary(p);s=0;for(k=1,#v,s+=if(v[k]==1,+1,-1));if(s<=6,print1(p,", "))) \\ Washington Bomfim, Jan 13 2011

A095316 Primes in whose binary expansion the number of 1-bits is > number of 0-bits minus 2.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 263, 269, 271, 277, 281

Offset: 1

Antti Karttunen, Jun 04 2004

Differs from primes (A000040) first time at n=32, where a(32)=139, while A000040(32)=131, as 131 whose binary expansion is 10000011, with 3 1-bits and 5 0-bits is the first prime excluded from this sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095317 in A000040. Subset of A095320. Subset: A095074. Cf. also A095326.

Select[Prime[Range[60]],DigitCount[#,2,1]>(DigitCount[#,2,0]-2)&] (* Harvey P. Dale, May 28 2012 *)

forprime(p=2,281,v=binary(p);s=0;for(k=1,#v,s+=if(v[k]==1,+1,-1));if(s>-2,print1(p,", "))) \\ Washington Bomfim, Jan 13 2011

A095317 Primes in whose binary expansion the number of 1 bits is <= number of 0 bits minus 2.

Original entry on oeis.org

131, 137, 193, 257, 521, 523, 547, 577, 593, 641, 643, 673, 769, 773, 1031, 1033, 1049, 1061, 1091, 1093, 1097, 1153, 1217, 1283, 1289, 1297, 1409, 1553, 1601, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2113, 2129, 2131, 2137, 2153

Offset: 1

Antti Karttunen, Jun 04 2004

Harvey P. Dale, Table of n, a(n) for n = 1..1000
A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095316 in A000040. Subset: A095321. Subset of A095071. Cf. also A095327.

Select[Prime[Range[400]],DigitCount[#,2,1]<=DigitCount[#,2,0]-2&] (* Harvey P. Dale, Dec 10 2017 *)

forprime(p=2,2200,v=binary(p);s=0;for(k=1,#v,s+=if(v[k]==1,+1,-1));if(s<=-2,print1(p,", ")))
\\ Washington Bomfim, Jan 13 2011

A095318 Primes in whose binary expansion the number of 1 bits is > 3 + number of 0 bits.

Original entry on oeis.org

31, 47, 59, 61, 127, 191, 223, 239, 251, 367, 379, 383, 431, 439, 443, 463, 479, 487, 491, 499, 503, 509, 607, 631, 701, 719, 727, 733, 743, 751, 757, 761, 823, 827, 829, 859, 863, 877, 883, 887, 911, 919, 941, 947, 953, 967, 971, 983, 991

Offset: 1

Antti Karttunen, Jun 04 2004

A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095319 in A000040. Subset of A095314. Subset: A095322. Cf. also A095328.

B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
if(b1 > (3+b0), return(1);, return(0););};
forprime(x = 2, 991, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 12 2011

A095319 Primes in whose binary expansion the number of 1 bits is <= 3 + number of 0 bits.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, 53, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 211, 227, 229, 233, 241, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311

Offset: 1

Antti Karttunen

Differs from primes (A000040) first time at n=11, where a(11)=37, while A000040(11)=31, as 31 whose binary expansion is 11111, with 5 1-bits and no 0 bits is the first prime excluded from this sequence. - Jun 04 2004

A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095318 in A000040. Subset of A095323, subset: A095315. A095329.

Select[Prime[Range[70]],DigitCount[#,2,1]Harvey P. Dale, Feb 22 2020 *)

B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
if(b1 <= (3+b0), return(1);, return(0););};
forprime(x = 2, 311, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 12 2011

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A095283 Primes whose binary-expansion ends with an odd number of 1's.

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A095284 Primes in whose binary expansion the number of 1 bits is > 5 + number of 0 bits.

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A095285 Primes in whose binary expansion the number of 1 bits is <= 5 + number of 0 bits.

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A095287 Primes in whose binary expansion the number of 1-bits is <= 1 + number of 0-bits.

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A095312 Primes in whose binary expansion the number of 1-bits is > 6 + number of 0-bits.

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A095313 Primes in whose binary expansion the number of 1-bits is <= 6 + number of 0-bits.

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A095316 Primes in whose binary expansion the number of 1-bits is > number of 0-bits minus 2.

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A095317 Primes in whose binary expansion the number of 1 bits is <= number of 0 bits minus 2.

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A095318 Primes in whose binary expansion the number of 1 bits is > 3 + number of 0 bits.

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