A095323 -id:A095323 - cp's OEIS frontend

A095325 Number of A095323-primes in range ]2^n,2^(n+1)].

1, 2, 2, 4, 7, 12, 19, 30, 67, 102, 211, 340, 722, 1146, 2329, 3992, 8423, 14010, 29281, 49682, 105893, 180016, 378928, 654049, 1385920, 2387358, 5069466, 8820563, 18782814, 32732736, 69445570, 121964573, 259680216

Offset: 1

Antti Karttunen, Jun 04 2004

nonn

Ratios a(n)/A036378(n) converge as: 1, 1, 1, 0.8, 1, 0.923077, 0.826087, 0.697674, 0.893333, 0.744526, 0.827451, 0.732759, 0.827982, 0.710918, 0.768647, 0.699247, 0.783608, 0.687102, 0.757888, 0.675156, 0.754568, 0.671161, 0.737633, 0.663458, 0.731696, 0.654834, 0.721397, 0.650393, 0.716702, 0.645647, 0.70731, 0.640787, 0.703124

Ratios a(n)/A095054(n) converge as: 1, 1, 1, 1, 1, 1.2, 0.95, 0.9375, 1.030769, 1.051546, 1.039409, 1.017964, 1.005571,1.014159, 0.97816, 1.009866, 1.018993, 1.007117, 1.009864, 1.002381,1.003497, 1.006182, 1.005197, 1.005142, 1.001903, 1.002926, 1.004856,1.004575, 1.004471, 1.003502, 1.001392, 1.002787, 1.002428

A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence
Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]

a(n) = A036378(n)-A095324(n).

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

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

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

Antti Karttunen, Jun 04 2004

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

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

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 *)

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

cp's OEIS Frontend

A095325 Number of A095323-primes in range ]2^n,2^(n+1)].

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

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PARI

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

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Mathematica

PARI