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 1-4 of 4 results.

A095295 Number of A095285-primes in range ]2^n,2^(n+1)].

Original entry on oeis.org

1, 2, 2, 5, 7, 12, 19, 39, 67, 122, 211, 417, 722, 1376, 2329, 4846, 8423, 17092, 29281, 60653, 105893, 216916, 378928, 786408, 1385920, 2876617, 5069466, 10583728, 18782814, 39107151, 69445570, 145468029, 259680216
Offset: 1

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Comments

Ratios a(n)/A036378(n) converge as: 1, 1, 1, 1, 1, 0.923077, 0.826087, 0.906977, 0.893333, 0.890511, 0.827451, 0.898707, 0.827982, 0.853598, 0.768647, 0.848835, 0.783608, 0.838254, 0.757888, 0.824246, 0.754568, 0.808736, 0.737633, 0.797721, 0.731696, 0.789034, 0.721397, 0.780401, 0.716702, 0.771382, 0.70731, 0.764271, 0.703124
Ratios a(n)/A095326(n) converge as: 1, 1, 1, 1, 1, 0.923077, 0.95, 0.928571, 1.030769, 1, 1.039409, 1.012136, 1.005571, 0.973815, 0.97816, 0.997325, 1.018993, 1.00808, 1.009864, 1.002794,1.003497, 1.000397, 1.005197, 1.000665, 1.001903, 1.003022, 1.004856,1.00371, 1.004471, 1.001864, 1.001392, 1.001771, 1.002428

Links

Crossrefs

a(n) = A036378(n)-A095294(n). Cf. A095052, A095053.

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

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Links

Crossrefs

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

Programs

  • PARI
    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

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

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Comments

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.

Links

Crossrefs

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.

Programs

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

A095323 Primes in whose binary expansion the number of 1 bits is <= 4 + number of 0 bits.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 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, 293
Offset: 1

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Comments

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 five 1 bits and no 0 bits is the first prime excluded from this sequence. Note that 15 (1111 in binary) is not prime.

Links

Crossrefs

Complement of A095322 in A000040. Subset of A095285. subset: A095319. Cf. A095325.

Programs

  • Mathematica
    Select[Prime[Range[100]],DigitCount[#,2,1]<(5+DigitCount[#,2,0])&] (* Harvey P. Dale, Dec 09 2015 *)
  • PARI
    B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
if(b1 <= (4+b0), return(1);, return(0););};
forprime(x = 2, 293, if(B(x), print1(x, ", "); ); ); \\ Washington Bomfim, Jan 12 2011
Showing 1-4 of 4 results.

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