A080166 Primes having initial digits "11" in binary representation.

3, 7, 13, 29, 31, 53, 59, 61, 97, 101, 103, 107, 109, 113, 127, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 769, 773, 787, 797, 809, 811, 821

Offset

1,1

Comments

Also primes that terminate at 3,2,1 in the x-1 problem: Repeat, if x is even divide by 2 else subtract 1, until 3 is reached. - Cino Hilliard, Mar 27 2003

Or, primes in A004760. - Vladimir Shevelev, May 04 2009

Links

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

Example

A000040(16)=53 -> '110101' therefore 53 is a term.

Mathematica

Select[Prime[Range[200]], Take[IntegerDigits[#, 2], 2]=={1, 1}&] (* Harvey P. Dale, Jul 30 2019 *)

Prog

(PARI) pxnm1(n, p) = { forprime(x=2, n, p1 = x; while(p1>1, if(p1%2==0, p1/=2, p1 = p1*p-1; ); if(p1 == 3, break); ); if(p1 == 3, print1(x" ")) ) }

Crossrefs

Cf. A004676, A080168.

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

Column k=3 of A262365.

Sequence in context: A258349 A089726 A093575 * A116872 A161490 A283587

Adjacent sequences: A080163 A080164 A080165 * A080167 A080168 A080169

Keyword

nonn,base

Author

Reinhard Zumkeller, Feb 03 2003

Status

approved