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.

A095294 Number of A095284-primes in range ]2^n,2^(n+1)].

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 4, 4, 8, 15, 44, 47, 150, 236, 701, 863, 2326, 3298, 9354, 12933, 34443, 51300, 134780, 199410, 508200, 769127, 1957824, 2978179, 7424464, 11590386, 28737086, 44867556, 109643089
Offset: 1

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Comments

Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0, 0, 0.076923, 0.173913, 0.093023, 0.106667, 0.109489, 0.172549, 0.101293, 0.172018, 0.146402, 0.231353, 0.151165, 0.216392, 0.161746, 0.242112, 0.175754, 0.245432, 0.191264, 0.262367, 0.202279, 0.268304, 0.210966, 0.278603, 0.219599, 0.283298, 0.228618, 0.29269, 0.235729, 0.296876
Ratios a(n)/A095327(n) converge as: 1, 1, 1, 1, 1, 0,1.333333, 4., 0.8, 1, 0.846154, 0.903846, 0.974026, 1.18593, 1.080123,1.015294, 0.93677, 0.960116, 0.970332, 0.987101, 0.9894, 0.998326, 0.985673, 0.997384, 0.994846, 0.988856, 0.987642, 0.987035, 0.988865, 0.993762, 0.996653, 0.994302, 0.994296

Links

Crossrefs

a(n) = A036378(n)-A095295(n). Cf. also A095329, A095052, A095053.

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

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. Note that 63 (111111 in binary) is not prime.

Links

Crossrefs

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.

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 = 2, 283, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 12 2011

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

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)
  • PARI
    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

A095322 Primes in whose binary expansion the number of 1 bits is > 4 + number of 0 bits.

Original entry on oeis.org

31, 127, 191, 223, 239, 251, 367, 379, 383, 431, 439, 443, 463, 479, 487, 491, 499, 503, 509, 751, 863, 887, 983, 991, 1013, 1019, 1021, 1151, 1277, 1279, 1399, 1439, 1471, 1487, 1499, 1511, 1523, 1531, 1663, 1723, 1759, 1783, 1787, 1789, 1823
Offset: 1

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Links

Crossrefs

Complement of A095323 in A000040. Subset of A095318. Subset: A095284. Cf. also A095324.

Programs

  • Mathematica
    btsQ[n_]:=Module[{idn2=IntegerDigits[n,2]},Count[idn2,1]>4+Count[ idn2,0]]; Select[Prime[Range[300]],btsQ] (* Harvey P. Dale, Nov 12 2011 *)
  • 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, 1823, if(B(x), print1(x, ", "); ); ); \\ Washington Bomfim, Jan 12 2011
Showing 1-4 of 4 results.

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