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.

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

Links

Table of n, a(n) for n=2..49.

Christian Krause, LODA program

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

Cf. A007504, A034956, A061802.

Sequence in context: A063757 A193711 A079328 * A227621 A060064 A045474

Adjacent sequences: A073609 A073610 A073611 * A073613 A073614 A073615

Keyword

nonn

Author

Amarnath Murthy, Aug 05 2002

Extensions

Edited by Robert G. Wilson v and T. D. Noe, Aug 08 2002

Status

approved