A109277 Slowest increasing sequence in which a(n) is a prime closest to the sum of all previous terms.

2, 2, 3, 7, 13, 29, 53, 109, 223, 439, 881, 1759, 3517, 7039, 14071, 28151, 56299, 112601, 225217, 450413, 900821, 1801669, 3603317, 7206631, 14413253, 28826519, 57653027, 115306073, 230612149, 461224289, 922448587, 1844897167, 3689794321, 7379588659, 14759177311

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Example

a(1)=2, sum(1)=2; prime closest to sum is 2, hence a(2)=2, sum(2)=4; there are two primes 3 and 5 closest to sum(2), we choose the smallest one, hence a(3)=3, sum(3)=7, etc.

Maple

s:= proc(n) option remember; `if`(n<1, 0, s(n-1)+a(n)) end:
a:= proc(n) option remember; `if`(n=1, 2, (h-> ((p, q)->
     `if`(q-h<h-p, q, p))(prevprime(h+1), nextprime(h-1)))(s(n-1)))
    end:
seq(a(n), n=1..35);  # Alois P. Heinz, Jan 14 2026

Mathematica

s={2}; su=2; Do[If[PrimeQ[su], a=su, pp=PrimePi[su]; prv=Prime[pp]; nxt=Prime[pp+1]; a=If[su-prv>nxt-su, nxt, prv]]; AppendTo[s, a]; Print[a]; su+=a, {i, 42}]; s

Crossrefs

Cf. A109278.

Sequence in context: A167348 A068524 A184841 * A093437 A075059 A060357

Adjacent sequences: A109274 A109275 A109276 * A109278 A109279 A109280

Keyword

nonn

Author

Zak Seidov, Jun 25 2005

Extensions

Definition and comment clarified by Jonathan Sondow, Jun 16 2012

Status

approved