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A073612
Group the positive integers as (1, 2), (3, 4, 5), (6, 7, 8, 9, 10), (11, 12, 13, 14, 15, 16, 17), ... the n-th group containing prime(n) elements. Except the first, all groups contain an odd number of elements and hence have a middle term. Sequence gives the middle terms starting from group 2.
2
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
OFFSET
2,1
FORMULA
Difference of the triangular numbers corresponding to the sum of first (n+1) primes and that of first n primes/prime(n) for n > 1.
a(n) = (A061802(n-1) + 1)/2. - Hugo Pfoertner, Apr 30 2021
a(n) = A007504(n) - (prime(n)-1)/2. - Andrew Howroyd, Apr 30 2021
a(n) = (Sum_{i=2..n-1} A001043(i)) / 2 + 4. - Christian Krause, May 06 2021
MATHEMATICA
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
Module[{nn=50, no, pr}, no=Total[Prime[Range[2, nn+1]]]; pr=Prime[Range[2, nn]]; #[[ (Length[ #]+1)/2]]&/@TakeList[Range[3, no], pr]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Sep 20 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Aug 05 2002
EXTENSIONS
Edited by Robert G. Wilson v and T. D. Noe, Aug 08 2002
STATUS
approved