A095324 -id:A095324 - cp's OEIS frontend

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

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

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

Original entry on oeis.org

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).

cp's OEIS Frontend

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

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