A080165 Primes having initial digits "10" in binary representation.

2, 5, 11, 17, 19, 23, 37, 41, 43, 47, 67, 71, 73, 79, 83, 89, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 521, 523, 541, 547, 557, 563

Offset

1,1

Comments

Also primes that terminate at 4,2,1 in the x-1 problem: Repeat, if x is even divide by 2 else subtract 1, until 4 is reached. - Cino Hilliard, Mar 27 2003

David W. Wilson remarks that it follows from standard results about primes in short intervals (see for example Harman, 1982) that there are infinitely many numbers in any base b starting with any nonzero prefix c. - N. J. A. Sloane, Sep 19 2015

Links

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

G. Harman, Primes in short intervals, Math. Zeit., 180 (1982), 335-348.

Example

A000040(15)=47 -> '101111' therefore 47 is a term.

Mathematica

Select[Prime[Range[1000]], IntegerDigits[#, 2][[;; 2]] == {1, 0}&] (* Jean-François Alcover, Oct 25 2021 *)

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 == 4, break); ); if(p1 == 4, print1(x" ")) ) }

Crossrefs

Cf. A004676, A080167.

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=2 of A262365.

Sequence in context: A132121 A070957 A166744 * A239712 A379541 A224363

Adjacent sequences: A080162 A080163 A080164 * A080166 A080167 A080168

Keyword

nonn,base

Author

Reinhard Zumkeller, Feb 03 2003

Status

approved