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A118538
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Let gap[n] = (Prime[n + 1] - Prime[n])/2. Then a(n) = Ceiling[Sum[gap[k] + Floor[Sqrt[gap[k]^2 + 1]], {k, 1, n}]] - 5.
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0
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-3, -1, 1, 5, 7, 11, 13, 17, 23, 25, 31, 35, 37, 41, 47, 53, 55, 61, 65, 67, 73, 77, 83, 91, 95, 97, 101, 103, 107, 121, 125, 131, 133, 143, 145, 151, 157, 161, 167, 173, 175, 185, 187, 191, 193, 205, 217, 221, 223, 227, 233, 235, 245, 251, 257, 263, 265, 271, 275, 277, 287, 301, 305, 307, 311, 325, 331, 341, 343, 347
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Sequence has hyperbolic sinh functional structure using the gap function: gap[n]=Sinh[f[n]*n] via the identity ArcSinh[x]=Log[x+Sqrt[x^2+1]].
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MATHEMATICA
| gap[n_] = (Prime[n + 1] - Prime[n])/2 f[n_] := Ceiling[Sum[gap[k] + Floor[Sqrt[gap[k]^2 + 1]], {k, 1, n}]] - 5 aout = Table[f[n], {n, 1, 200}]
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CROSSREFS
| Sequence in context: A047969 A047812 A129392 * A141523 A201588 A086385
Adjacent sequences: A118535 A118536 A118537 * A118539 A118540 A118541
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KEYWORD
| sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 06 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 01 2006
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