A054408 a(n) = smallest positive integer not already in sequence such that the partial sum a(1)+...+a(n) is prime.

2, 1, 4, 6, 10, 8, 12, 16, 14, 24, 30, 22, 18, 26, 34, 36, 20, 28, 38, 40, 32, 42, 46, 48, 44, 52, 56, 60, 54, 58, 66, 50, 64, 62, 70, 84, 90, 72, 92, 76, 86, 94, 74, 88, 68, 82, 80, 102, 96, 100, 114, 98, 78, 112, 120, 110, 108, 106, 126, 122, 130, 132, 134, 124, 128, 118

Offset

1,1

Comments

1 is the only odd number in this sequence. - Derek Orr, Feb 07 2015

Conjecture: Every even number appears. - N. J. A. Sloane, May 29 2017

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..4100 from N. J. A. Sloane).

Mathematica

t = {2}; Do[i = 1; While[! PrimeQ[Total[t] + i] || MemberQ[t, i], i++]; AppendTo[t, i], {65}]; t (* Jayanta Basu, Jul 04 2013 *)

Prog

(PARI) v=[2]; n=1; while(n<100, if(isprime(vecsum(v)+n)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0); n++); v \\ Derek Orr, Feb 07 2015
(Python)
from sympy import isprime
def aupton(terms):
    alst, aset, asum = [], set(), 0
    while len(alst) < terms:
        an = 1
        while True:
            while an in aset: an += 1
            if isprime(asum + an):
                alst, aset, asum = alst + [an], aset | {an}, asum + an
                break
            an += 1
    return alst
print(aupton(66)) # Michael S. Branicky, Jun 05 2021

Crossrefs

Cf. A254337, A291544 (partial sums).

See A073659 and A390314 for another version.

In A055265 only pairs of adjacent terms add to primes.

Sequence in context: A338746 A283309 A366043 * A285637 A205845 A034424

Adjacent sequences: A054405 A054406 A054407 * A054409 A054410 A054411

Keyword

nonn,easy

Author

Henry Bottomley, May 09 2000

Status

approved