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A101264 a(n) = 1 if 2*n + 1 is prime, otherwise a(n) = 0.

%I A101264 #47 Sep 08 2022 08:45:16
%S A101264 0,1,1,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,
%T A101264 0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0,
%U A101264 1,1,0,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0,0
%N A101264 a(n) = 1 if 2*n + 1 is prime, otherwise a(n) = 0.
%C A101264 Inverse Mobius transform of the sequence, after dropping a(0), yields A086668. - _R. J. Mathar_, Jan 25 2009
%C A101264 If we drop a(0) then we may describe the sequence as: for all numbers k(n) [k(n) = 4 ceiling(n/2) + (-1)^n] congruent to -1 or +1 (mod 4) starting with k(n) = {3,5,7,9,11,...}, a(k(n)) is 1 if k(n) is prime and 0 if k(n) is composite. - _Daniel Forgues_, Mar 01 2009
%D A101264 D. H. Lehmer, "Computer Technology Applied to the Theory of Numbers," from Studies in Number Theory, ed. William J. LeVeque. Englewood Cliffs, New Jersey: Prentice Hall (1969): 138.
%H A101264 Daniel Forgues, <a href="/A101264/b101264.txt">Table of n, a(n) for n=0..49999</a>
%F A101264 a(n) = A057427(A085090(n+1)). - _Reinhard Zumkeller_, Sep 14 2006
%F A101264 For n > 0, a(n) = (2n-1)! mod (2n+1). - _Thomas Ordowski_, Jul 23 2016
%F A101264 a(n) = pi(2*n+1) - pi(2*n), where pi(n) = A000720(n). - _Ridouane Oudra_, Aug 25 2019
%e A101264 a(1) = 1 because 2*1+1 = 3 is prime;
%e A101264 a(2) = 1 because 2*2+1 = 5 is prime;
%e A101264 a(3) = 1 because 2*3+1 = 7 is prime;
%e A101264 a(4) = 0 because 2*4+1 = 9 is composite.
%p A101264 with(numtheory): a:= proc(n) if isprime(2*n+1)=true then 1 else 0 fi end:
%p A101264 seq(a(n), n=0..80); # _Ridouane Oudra_, Aug 25 2019
%t A101264 Table[If[PrimeQ[2n + 1], 1, 0], {n, 0, 104}] (* _Ray Chandler_, Jan 09 2005 *)
%t A101264 Table[Boole[PrimeQ[n]], {n, 1, 209, 2}] (* _Alonso del Arte_, Sep 25 2012 *)
%o A101264 (Magma) [IsPrime(2*n+1) select 1 else 0: n in [1..100]]; // _Marius A. Burtea_, Aug 25 2019
%o A101264 (PARI) first(n) = {my(res = vector(n)); forprime(p = 3, 2*n - 1, res[p \ 2] = 1); res} \\ _David A. Corneth_, Aug 25 2019
%Y A101264 Bisection (odd n) of A010051.
%Y A101264 Cf. A065091, A063524, A000720.
%Y A101264 If we drop a(0), equals absolute value of A156707. - _Daniel Forgues_, Mar 01 2009
%K A101264 easy,nonn
%O A101264 0,1
%A A101264 _Giovanni Teofilatto_, Dec 18 2004
%E A101264 Corrected by _Ray Chandler_, Jan 09 2005