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

Author

Henry Bottomley, May 09 2000

Keywords

• nonn
• easy

Comments

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

Conjecture: Every even numbers 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).

Crossrefs

Cf. A254337.

See A073659 for another version.

In A055265 only pairs of adjacent terms add to primes.

Programs

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 *)

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