A139312 - OEIS

%I #13 Jan 25 2015 21:36:03

%S 0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,

%T 0,1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,

%U 0,0,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0

%N Characteristic function of the good primes (version 1).

%C a(n)=1 if prime(n)^2 - prime(n-1)*prime(n+1) >=0, else a(n)=0.

%F a(n) = 1 if A056221(n-1)<=0, else a(n)=0.

%t f[n_] := If[ Prime[n]^2 - Prime[n - 1]*Prime[n + 1] > 0, 1, 0]; Array[f, 105, 2] (*alternative formula: derived*) Solve[x^2 - (x - a)*(x + b) == 0, x]; a = -Prime[n - 1] + Prime[n]; b = -Prime[n] + Prime[n + 1]; f[n_] = If[-Prime[-1 + n] + 2 Prime[n] - Prime[1 + n] == 0, 0, a*b/(b - a)]; Table[ If[ f[n] > 0, 0, 1], {n, 2, 106}]

%t If[#[[2]]^2-(#[[1]]#[[3]])>=0,1,0]&/@Partition[Prime[Range[110]],3,1] (* _Harvey P. Dale_, Jan 25 2015 *)

%o (PARI) a(n)=my(p=prime(n));p^2>=precprime(p-1)*nextprime(p+1) \\ _Charles R Greathouse IV_, Jun 24, 2011

%Y Cf. A056221, A046869, A068828.

%K nonn,easy

%O 2,1

%A _Roger L. Bagula_, Jun 07 2008

%E All entries corrected. - _R. J. Mathar_, _Charles R Greathouse IV_  _Robert G. Wilson v_, Jun 16 2011