A095312 -id:A095312 - cp's OEIS frontend

A095332 Number of A095312-primes in range ]2^n,2^(n+1)].

0, 0, 0, 0, 0, 1, 0, 4, 3, 15, 9, 47, 73, 236, 251, 863, 1180, 3298, 4284, 12933, 18598, 51300, 73371, 199410, 292156, 769127, 1131645, 2978179, 4533090, 11590386, 17623347, 44867556, 69537472

Offset: 1

Antti Karttunen, Jun 04 2004

nonn

Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0, 0, 0.076923, 0, 0.093023, 0.04, 0.109489, 0.035294, 0.101293, 0.083716, 0.146402, 0.082838, 0.151165, 0.109778, 0.161746, 0.110884, 0.175754, 0.132525, 0.191264, 0.142826, 0.202279, 0.154244, 0.210966, 0.161036, 0.219599, 0.172971, 0.228618, 0.179496, 0.235729, 0.188283

Ratios a(n)/A095331(n) converge as: 1, 1, 1, 1, 1, 0, 1,4, 0.75, 1, 0.642857, 0.903846, 0.879518, 1.18593, 0.965385,1.015294, 0.980066, 0.960116, 0.932115, 0.987101, 0.973972, 0.998326,1.012223, 0.997384, 0.985958, 0.988856, 0.981798, 0.987035, 0.991666, 0.993762, 0.991831, 0.994302, 0.992846

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)-A095333(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

Antti Karttunen, Jun 04 2004

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

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

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

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.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

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.

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

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

cp's OEIS Frontend

A095332 Number of A095312-primes in range ]2^n,2^(n+1)].

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A095284 Primes in whose binary expansion the number of 1 bits is > 5 + number of 0 bits.

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PARI

A095313 Primes in whose binary expansion the number of 1-bits is <= 6 + number of 0-bits.

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Mathematica

PARI