A109278 Fastest increasing sequence in which a(n) is a prime closest to the sum of all previous terms.

2, 2, 5, 11, 19, 41, 79, 157, 317, 631, 1259, 2521, 5039, 10079, 20161, 40343, 80669, 161333, 322669, 645329, 1290673, 2581349, 5162681, 10325369, 20650753, 41301493, 82602997, 165205981, 330411959, 660823921, 1321647869, 2643295709, 5286591421, 10573182853

Offset

1,1

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..2222

Formula

Limit_{n->oo} a(n)/a(n-1) = 2. - Bruce Nye, Jan 14 2026

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 largest one, hence a(3)=5, 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, p, q))(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, prv, nxt]]; AppendTo[s, a]; Print[a]; su+=a, {i, 42}]; s

Prog

(PARI)
my(N=40, v=vector(N), s=2); v[1]=s; for(n=2, N, my(lo=precprime(s), hi=nextprime(s)); v[n]=if(s-lo<hi-s, lo, hi); s+=v[n]); v \\ Bruce Nye, Jan 14 2026

Crossrefs

Cf. A109277.

Sequence in context: A375317 A336269 A078405 * A367966 A112527 A216642

Adjacent sequences: A109275 A109276 A109277 * A109279 A109280 A109281

Keyword

nonn

Author

Zak Seidov, Jun 25 2005

Extensions

Definition and comment clarified by Jonathan Sondow, Jun 16 2012

Status

approved