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