A095332 -id:A095332 - cp's OEIS frontend

A095312 Primes in whose binary expansion the number of 1-bits is > 6 + number of 0-bits.

127, 383, 479, 503, 509, 991, 1019, 1021, 1279, 1471, 1531, 1663, 1759, 1783, 1787, 1789, 1951, 1979, 1999, 2011, 2027, 2029, 2039, 3067, 3581, 3583, 3823, 3967, 4027, 4079, 4091, 4093, 5087, 5119, 5503, 5623, 5879, 6007, 6011, 6047

Offset: 1

Antti Karttunen, Jun 04 2004

Harvey P. Dale, Table of n, a(n) for n = 1..10000
A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095313 in A000040. Subset of A095284. Cf. also A095332.

n1bQ[n_]:=Module[{idn2=IntegerDigits[n,2]},Count[idn2,1]>6+Count[idn2,0]]; Select[Prime[Range[1000]],n1bQ] (* Harvey P. Dale, Jun 25 2014 *)

forprime(p=2,6100,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

A095333 Number of A095313-primes in range [2^n,2^(n+1)].

Original entry on oeis.org

1, 2, 2, 5, 7, 12, 23, 39, 72, 122, 246, 417, 799, 1376, 2779, 4846, 9569, 17092, 34351, 60653, 121738, 216916, 440337, 786408, 1601964, 2876617, 5895645, 10583728, 21674188, 39107151, 80559309, 145468029, 299785833

Offset: 1

Antti Karttunen, Jun 04 2004

nonn

Ratios a(n)/A036378(n) converge as: 1, 1, 1, 1, 1, 0.923077, 1, 0.906977, 0.96, 0.890511, 0.964706, 0.898707, 0.916284, 0.853598, 0.917162, 0.848835, 0.890222, 0.838254, 0.889116, 0.824246, 0.867475, 0.808736, 0.857174, 0.797721, 0.845756, 0.789034, 0.838964, 0.780401, 0.827029, 0.771382, 0.820504, 0.764271, 0.811717

Ratios a(n)/A095330(n) converge as: 1, 1, 1, 1, 1, 0.923077, 1, 0.928571, 1.014085, 1, 1.020747, 1.012136, 1.012674, 0.973815, 1.003249, 0.997325, 1.002514, 1.00808, 1.009166, 1.002794,1.004099, 1.000397, 0.997992, 1.000665, 1.002604, 1.003022, 1.003571,1.00371, 1.001761, 1.001864, 1.001805, 1.001771, 1.001674

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)-A095332(n).

cp's OEIS Frontend

A095312 Primes in whose binary expansion the number of 1-bits is > 6 + number of 0-bits.

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