A095320 -id:A095320 - cp's OEIS frontend

A095330 Number of A095320-primes in range ]2^n,2^(n+1)].

1, 2, 2, 5, 7, 13, 23, 42, 71, 122, 241, 412, 789, 1413, 2770, 4859, 9545, 16955, 34039, 60484, 121241, 216830, 441223, 785885, 1597803, 2867949, 5874665, 10544609, 21636090, 39034399, 80414166, 145210901, 299284792

Offset: 1

Antti Karttunen, Jun 04 2004

nonn

Ratios a(n)/A036378(n) converge as: 1, 1, 1, 1, 1, 1, 1, 0.976744, 0.946667, 0.890511, 0.945098, 0.887931, 0.904817, 0.876551, 0.914191, 0.851112, 0.88799, 0.831535, 0.881041, 0.82195, 0.863934, 0.808416, 0.858898, 0.797191, 0.84356, 0.786657, 0.835979, 0.777517, 0.825576, 0.769947, 0.819026, 0.76292, 0.81036

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)-A095331(n).

A095316 Primes in whose binary expansion the number of 1-bits is > number of 0-bits minus 2.

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, 127, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 263, 269, 271, 277, 281

Offset: 1

Antti Karttunen, Jun 04 2004

Differs from primes (A000040) first time at n=32, where a(32)=139, while A000040(32)=131, as 131 whose binary expansion is 10000011, with 3 1-bits and 5 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 A095317 in A000040. Subset of A095320. Subset: A095074. Cf. also A095326.

Select[Prime[Range[60]],DigitCount[#,2,1]>(DigitCount[#,2,0]-2)&] (* Harvey P. Dale, May 28 2012 *)

forprime(p=2,281,v=binary(p);s=0;for(k=1,#v,s+=if(v[k]==1,+1,-1));if(s>-2,print1(p,", "))) \\ Washington Bomfim, Jan 13 2011

A095321 Primes in whose binary expansion the number of 1-bits is <= number of 0-bits minus 3.

Original entry on oeis.org

257, 521, 577, 641, 769, 1031, 1033, 1049, 1061, 1091, 1093, 1097, 1153, 1217, 1283, 1289, 1297, 1409, 1553, 1601, 2053, 2069, 2081, 2083, 2089, 2113, 2129, 2179, 2309, 2593, 2689, 3089, 3137, 3329, 4099, 4111, 4129, 4133, 4139, 4153

Offset: 1

Antti Karttunen, Jun 04 2004

Robert Israel, 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 A095320 in A000040. Subset of A095317. Cf. also A095331.

filter:= proc(p) local L;
  L:= convert(p,base,2);
  2*convert(L,`+`) <= nops(L)-3
end proc;
select(filter, [seq(ithprime(i),i=1..1000)]); # Robert Israel, Apr 27 2025

Select[Prime[Range[600]],DigitCount[#,2,1]<=DigitCount[#,2,0]-3&] (* Harvey P. Dale, Jul 04 2018 *)

forprime(p=2, 4200, v=binary(p); s=0; for(k=1,#v, s+=if(v[k]==1,+1,-1)); if(s<=-3, print1(p,", "))) \\ Washington Bomfim, Jan 12 2011

cp's OEIS Frontend

A095330 Number of A095320-primes in range ]2^n,2^(n+1)].

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A095316 Primes in whose binary expansion the number of 1-bits is > number of 0-bits minus 2.

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Mathematica

PARI

A095321 Primes in whose binary expansion the number of 1-bits is <= number of 0-bits minus 3.

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Author

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Crossrefs

Programs

Maple

Mathematica

PARI