A262285 Primes whose binary expansion begins 111.

7, 29, 31, 59, 61, 113, 127, 227, 229, 233, 239, 241, 251, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873

Offset: 1

Author

N. J. A. Sloane, Sep 19 2015

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Primes whose binary expansion begins with binary expansion of 1, 2, 3, 4, 5, 6, 7: A000040, A080165, A080166, A262286, A262284, A262287, A262285.

Suggested by A262350.

Column k=7 of A262365.

Programs

Maple

lis:=[]; q:=7;
for i from 1 to 10 do for j from 1 to 2^i-1 do
if isprime(q*2^i+j) then lis:=[op(lis),q*2^i+j]; fi; od: od:
lis;

Mathematica

Select[FromDigits[#,2]&/@(Join[{1,1,1},#]&/@Flatten[Table[Tuples[{0,1},n],{n,0,8}],1]),PrimeQ] (* or *) Select[Prime[Range[ 3,350]],Take[ IntegerDigits[ #,2],3]=={1,1,1}&] (* Harvey P. Dale, May 02 2021 *)