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A139312 Characteristic function of the good primes (version 1). 0
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 (list; graph; refs; listen; history; text; internal format)
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 A285685 A287773

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

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Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)