A198519 a(2*k) is the sum of the prior 3 terms, k>1, with all sequence terms minimal distinct primes, a(1)=3, a(2)=5.

3, 5, 11, 19, 7, 37, 17, 61, 23, 101, 13, 137, 29, 179, 31, 239, 41, 311, 67, 419, 71, 557, 73, 701, 47, 821, 43, 911, 59, 1013, 79, 1151, 53, 1283, 97, 1433, 83, 1613, 127, 1823, 89, 2039, 109, 2237, 113, 2459, 139, 2711, 103, 2953, 107, 3163, 163, 3433, 131, 3727, 149, 4007, 181, 4337, 173, 4691

Offset

1,1

Comments

Previous name was: a(2n-1) is the first unused prime which is the sum of the two preceding terms and such that a(2n) is that sum and it is also an unused prime.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Example

a(3) does not equal 7 since 3+5+7 which is 15 is not a prime, but the next prime, 11, meets the criteria.

Mathematica

s = {3, 5}; k = 1; While[k < 31, p = s[[-2]] + s[[-1]]; q = 7; While[ !PrimeQ[p + q] || MemberQ[s, q] || MemberQ[s, p + q], q = NextPrime@ q]; AppendTo[s, q]; AppendTo[s, p + q]; k++]; s

Crossrefs

Cf. A073653, A084331, A101595.

Sequence in context: A320351 A319641 A306895 * A045957 A364962 A153065

Adjacent sequences: A198516 A198517 A198518 * A198520 A198521 A198522

Keyword

easy,nonn

Author

Robert G. Wilson v, Dec 21 2012

Extensions

Name changed by Bill McEachen, Mar 13 2026

Status

approved