A073659 a(1) = 1; for n > 1, a(n) is the smallest even number not already in the sequence such that a(1) + ... + a(n) is a prime.

1, 2, 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

Amarnath Murthy, Aug 10 2002

Keywords

• nonn
• easy

Comments

Essentially the same as A054408. - R. J. Mathar, Dec 15 2008

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..4097 from N. J. A. Sloane).

Crossrefs

Cf. A054408, A073660.

See A055265 for a version where the sums of two adjacent terms are primes.

Programs

Mathematica

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

PARI

v=[1];n=1;while(n<200,if(isprime(n+vecsum(v))&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ Derek Orr, Jun 01 2015

Extensions

More terms from Sascha Kurz, Jan 28 2003

Offset corrected by Chai Wah Wu, Aug 27 2017