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A139312
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Characteristic function of the good primes (version 1).
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0
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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
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OFFSET
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2,1
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COMMENTS
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a(n)=1 if prime(n)^2 - prime(n-1)*prime(n+1) >=0, else a(n)=0.
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LINKS
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Table of n, a(n) for n=2..106.
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FORMULA
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a(n) = 1 if A056221(n-1)<=0, else a(n)=0.
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MATHEMATICA
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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}]
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PROG
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(PARI) a(n)=my(p=prime(n)); p^2>=precprime(p-1)*nextprime(p+1) \\ Charles R Greathouse IV, Jun 24, 2011
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CROSSREFS
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Cf. A056221, A046869, A068828.
Sequence in context: A141743 A112416 A061265 * A173923 A125122 A000035
Adjacent sequences: A139309 A139310 A139311 * A139313 A139314 A139315
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Roger L. Bagula, Jun 07 2008
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EXTENSIONS
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All entries corrected. - R. J. Mathar, C. Greathouse, R. G. Wilson v., Jun 16 2011
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STATUS
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approved
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