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Search: id:A073612
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| A073612 |
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Group the natural numbers as (1, 2), (3, 4, 5), (6, 7, 8, 9, 10), (11, 12, 13, 14, 15, 16, 17), ...each group containing p(n) elements. Barring the first, all groups contain odd number of elements and hence have a middle term. Sequence gives middle terms starting from group 2. |
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+0
1
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| 4, 8, 14, 23, 35, 50, 68, 89, 115, 145, 179, 218, 260, 305, 355, 411, 471, 535, 604, 676, 752, 833, 919, 1012, 1111, 1213, 1318, 1426, 1537, 1657, 1786, 1920, 2058, 2202, 2352, 2506, 2666, 2831, 3001, 3177, 3357, 3543, 3735, 3930, 4128, 4333, 4550, 4775
(list; graph; listen)
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OFFSET
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2,1
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FORMULA
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Difference of the triangular numbers corresponding to the sum of first (n+1) primes and that of first n primes/p(n) for n > 1.
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MATHEMATICA
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Table[ Sum[ Prime[i], {i, 1, n}] - Floor[ Prime[n]/2], {n, 2, 50}]
For[lst={}; n1=3; n=2, n<=100, n++, n2=n1+Prime[n]; AppendTo[lst, (n2+n1-1)/2]; n1=n2]; lst
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CROSSREFS
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Cf. A034956.
Sequence in context: A049628 A063757 A079328 this_sequence A060064 A045474 A131831
Adjacent sequences: A073609 A073610 A073611 this_sequence A073613 A073614 A073615
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 05 2002
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com) and T. D. Noe (noe(AT)sspectra.com), Aug 08 2002
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