A139312 Characteristic function of the good primes (version 1).

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, 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, 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

Offset: 2

Author

Roger L. Bagula, Jun 07 2008

Keywords

• nonn
• easy

Comments

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

Crossrefs

Cf. A056221, A046869, A068828.

Programs

Mathematica

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

PARI

a(n)=my(p=prime(n));p^2>=precprime(p-1)*nextprime(p+1) \\ Charles R Greathouse IV, Jun 24 2011

Formula

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

Extensions

All entries corrected. - R. J. Mathar, Charles R Greathouse IV Robert G. Wilson v, Jun 16 2011