

A080165


Primes having initial digits "10" in binary representation.


12



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
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OFFSET

1,1


COMMENTS

Also primes that terminate at 4,2,1 in the x1 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), 335348.


EXAMPLE

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


PROG

(PARI) pxnm1(n, p) = { forprime(x=2, n, p1 = x; while(p1>1, if(p1%2==0, p1/=2, p1 = p1*p1; ); 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 A224363 A307508
Adjacent sequences: A080162 A080163 A080164 * A080166 A080167 A080168


KEYWORD

nonn,base


AUTHOR

Reinhard Zumkeller, Feb 03 2003


STATUS

approved



