A073653 a(1)=3, a(2)=5; for n > 2, a(n) = smallest prime not included earlier such that a(n-2) + a(n-1) + a(n) is a prime.

3, 5, 11, 7, 13, 17, 23, 19, 29, 31, 37, 41, 53, 43, 61, 47, 59, 67, 71, 73, 79, 89, 83, 97, 101, 109, 103, 137, 107, 139, 113, 127, 149, 157, 151, 131, 167, 163, 173, 211, 179, 181, 197, 191, 199, 223, 239, 229, 193, 251, 233, 277, 241, 269, 263, 307, 227, 293

Offset

1,1

Comments

Primes which are less than some previous term: 7, 19, 43, 47, 83, 103, 107, 113, ...

In the first 10000 terms the range of the differences between primepi(a(i)) and (i+1) is from -39 to 78.

In the first 10000 terms the range of the differences between a(i) and the (i+1)th prime is from -416 to 912.

Conjecture: Every odd prime eventually appears; a(n) ~ prime(n).

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Example

a(3)=11 because 3 + 5 + 7 = 15 is composite and 3 + 5 + 11 = 19 is prime.

Mathematica

f[s_List] := Block[{p = s[[-2]] + s[[-1]], q = 7}, While[ !PrimeQ[p + q] || MemberQ[s, q], q = NextPrime[q]]; Append[s, q]]; Nest[f, {3, 5}, 56] (* Robert G. Wilson v, Mar 19 2012 *)

Crossrefs

Cf. A073654.

Sequence in context: A132162 A168323 A154561 * A225487 A145398 A087322

Adjacent sequences: A073650 A073651 A073652 * A073654 A073655 A073656

Keyword

nonn

Author

Amarnath Murthy, Aug 10 2002

Extensions

More terms from Sascha Kurz, Jan 28 2003

Status

approved