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Search: id:A139312
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| A139312 |
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An binary "appearance" or frequency sequence for good and bad primes: A028388 and A130903: a(n)=If[ Prime[n]^2-Prime[n-1]*Prime[n+1]>=0,1,0]. |
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+0
1
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| 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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When the sequence of gaps repeats, the f[n] function
comes up "ComplexInfinity": those are singularities of a=b in the derivation of when in the function f[n]:
-Prime[ -1 + n] + 2 Prime[n] - Prime[1 + n] == 0
Those are "bad primes".
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FORMULA
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Starting at 3: a(n)=If[ Prime[n]^2-Prime[n-1]*Prime[n+1]>=0,1,0]
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MATHEMATICA
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b0 = Table[If[Prime[n]^2 - Prime[n - 1]*Prime[n + 1] < 0, 1, 0], {n, 2, 100}] (*alternative formula: derived*) Solve[x^2 - (x - a)*(x + b) == 0, x] a = -Prime[ -1 + n] + Prime[n] b = -Prime[n] + Prime[1 + n] f[n_] = If[ -Prime[ -1 + n] + 2 Prime[n] - Prime[1 + n] == 0, 0, -a*b/(a - b)] a0 = Table[If[f[n] > 0, 1, 0], {n, 2, 100}]
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CROSSREFS
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Cf. A028388, A130903.
Sequence in context: A071023 A132194 A092079 this_sequence A071041 A140074 A090174
Adjacent sequences: A139309 A139310 A139311 this_sequence A139313 A139314 A139315
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 07 2008
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