A095329 -id:A095329 - cp's OEIS frontend

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

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

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

Antti Karttunen, Jun 04 2004

nonn

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

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

A095328 Number of A095318-primes in range ]2^n,2^(n+1)].

Original entry on oeis.org

0, 0, 0, 1, 3, 1, 4, 13, 32, 35, 96, 124, 335, 466, 1116, 1717, 4371, 6380, 15490, 23904, 58041, 88200, 209875, 331769, 795599, 1258386, 2951789, 4741344, 11144763, 17964801, 41781268, 68371012, 158643268

Offset: 1

Antti Karttunen, Jun 04 2004

nonn

Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0.2, 0.428571, 0.076923, 0.173913, 0.302326, 0.426667, 0.255474, 0.376471, 0.267241, 0.384174, 0.289082, 0.368317, 0.300753, 0.406642, 0.312898, 0.400932, 0.324844, 0.413586, 0.328839, 0.408549, 0.336542, 0.420036, 0.345166, 0.420047, 0.349607, 0.425255, 0.354353, 0.425546, 0.359213, 0.429551

Ratios a(n)/A095055(n) converge as: 1, 1, 1, 1, 1.5, 0.333333, 0.571429, 1.181818, 1.185185, 0.875, 1.2, 0.953846, 0.976676, 0.966805, 0.945763, 0.97779, 0.977197, 0.98472, 1.006694, 0.995088, 0.988538, 0.987616, 0.983496, 0.990015, 0.991634, 0.994496, 0.995506, 0.991599, 0.996345, 0.993681, 0.993649, 0.995067, 0.995042

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)-A095329(n).

cp's OEIS Frontend

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

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

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A095328 Number of A095318-primes in range ]2^n,2^(n+1)].

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