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 A080165 Primes having initial digits "10" in binary representation. 12

%I

%S 2,5,11,17,19,23,37,41,43,47,67,71,73,79,83,89,131,137,139,149,151,

%T 157,163,167,173,179,181,191,257,263,269,271,277,281,283,293,307,311,

%U 313,317,331,337,347,349,353,359,367,373,379,383,521,523,541,547,557,563

%N Primes having initial digits "10" in binary representation.

%C 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

%C 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

%H Alois P. Heinz, <a href="/A080165/b080165.txt">Table of n, a(n) for n = 1..20000</a>

%H G. Harman, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002426536">Primes in short intervals</a>, Math. Zeit., 180 (1982), 335-348.

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

%o (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" ")) ) }

%Y Cf. A004676, A080167.

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

%Y Column k=2 of A262365.

%K nonn,base

%O 1,1

%A _Reinhard Zumkeller_, Feb 03 2003

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Last modified September 15 14:49 EDT 2019. Contains 327078 sequences. (Running on oeis4.)