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.

A095324 Number of A095322-primes in range ]2^n,2^(n+1)].

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 4, 13, 8, 35, 44, 124, 150, 466, 701, 1717, 2326, 6380, 9354, 23904, 34443, 88200, 134780, 331769, 508200, 1258386, 1957824, 4741344, 7424464, 17964801, 28737086, 68371012, 109643089
Offset: 1

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Comments

Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0.2, 0, 0.076923, 0.173913, 0.302326, 0.106667, 0.255474, 0.172549, 0.267241, 0.172018, 0.289082, 0.231353, 0.300753, 0.216392, 0.312898, 0.242112, 0.324844, 0.245432, 0.328839, 0.262367, 0.336542, 0.268304, 0.345166, 0.278603, 0.349607, 0.283298, 0.354353, 0.29269, 0.359213, 0.296876
Ratios a(n)/A095019(n) converge as: 1, 1, 1, 1, 1, 0.333333, 1.333333, 1.181818, 0.8, 0.875, 0.846154, 0.953846, 0.974026, 0.966805, 1.080123, 0.97779, 0.93677, 0.98472, 0.970332, 0.995088, 0.9894, 0.987616, 0.985673, 0.990015, 0.994846, 0.994496, 0.987642, 0.991599, 0.988865, 0.993681, 0.996653, 0.995067, 0.994296

Links

Crossrefs

a(n) = A036378(n)-A095325(n).

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

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

Views

Author

Antti Karttunen, Jun 04 2004

Keywords

Links

Crossrefs

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

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 > (3+b0), return(1);, return(0););};
forprime(x = 2, 991, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 12 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.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.