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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
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
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
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
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Feb 03 2003
STATUS
approved