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A062357
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a(n) = n*p(n+1)-(n+1)*p(n) = n*d(n)-p(n), where p(n) is the n-th prime and d(n) is the n-th prime-difference, A001223(n).
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2
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-1, 1, 1, 9, -1, 11, -3, 13, 31, -9, 35, 11, -15, 13, 43, 43, -25, 47, 9, -31, 53, 9, 55, 103, 3, -49, 5, -51, 7, 307, -3, 61, -71, 201, -79, 65, 65, -11, 67, 67, -97, 239, -105, -17, -107, 353, 353, -31, -129, -29, 73, -135, 289, 73, 73, 73, -155, 77, -41, -161, 327, 575, -55, -183, -53, 607, 71, 343, -209, -69, 73, 217
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| A sequence based on the solution of the equation: 1+(1+n)*prime(n)/x-n*prime(n+1)/x=0 for x. This is an irrational rotation-like sequence: the sequence is similar to a Beatty sequence. - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 06 2002
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| a(n) = nA000040(n+1)-(n+1)A000040(n) = nA001223(n)-A000040(n)
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EXAMPLE
| n = 10: a(10) = 10*31-11*29 = 310-319 = -9; n = 54: a(54) = 54*257-55*251 = 13878-13805 = 73; n = 55: a(55) = 55*263-56*257 = 14465-14392 = 73; consecutive terms are often equal to each other.
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MATHEMATICA
| Table[(Prime[w+1]-Prime[w])*w-Prime[w], {w, 1, 1024}]
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PROG
| (PARI) for(n=1, 100, print1((n+1)*prime(n)-n*prime(n+1), ", "))
(PARI) { for (n=1, 1000, write("b062357.txt", n, " ", n*prime(n + 1) - (n + 1)*prime(n)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 06 2009]
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CROSSREFS
| Cf. A000040, A001223, A062742, A062743.
Sequence in context: A093644 A164791 A107829 * A061215 A072448 A145966
Adjacent sequences: A062354 A062355 A062356 * A062358 A062359 A062360
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KEYWORD
| sign
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jul 13 2001
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