A095331 -id:A095331 - cp's OEIS frontend

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

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

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

Original entry on oeis.org

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).

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

Original entry on oeis.org

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).

cp's OEIS Frontend

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

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

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

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