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

2,1

Comments

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

Links

Table of n, a(n) for n=2..106.

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A056221, A046869, A068828.

Sequence in context: A276394 A215532 A191152 * A323239 A376451 A285685

Adjacent sequences: A139309 A139310 A139311 * A139313 A139314 A139315

Keyword

nonn,easy

Author

Roger L. Bagula, Jun 07 2008

Extensions

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

Status

approved