A062391 a(1) = 3, a(2) = 5; a(n+1) = smallest prime number > a(n) such that the sum of any three consecutive terms is a prime.

3, 5, 11, 13, 17, 23, 31, 43, 53, 61, 67, 71, 73, 79, 89, 101, 103, 107, 127, 139, 167, 173, 181, 193, 197, 211, 223, 227, 233, 241, 269, 277, 281, 349, 353, 359, 379, 433, 467, 499, 521, 523, 557, 577, 587, 613, 631, 743, 757, 769, 821, 827, 829, 883, 947

Offset

1,1

Comments

What is the longest string of consecutive primes? A derived sequence could be the start of the first occurrence of a string of n consecutive primes in this sequence.

See A072225 for relevant info and links. - Zak Seidov, Sep 14 2016

Links

Zak Seidov, Table of n, a(n) for n = 1..1000.

Example

After 43, the next term is 53, since 31 + 43 + 47 = 121 is not prime and 31 + 43 + 53 = 127 is prime.

Mathematica

a=3; b=5; lst={a, b}; Do[c=a+b+n; If[PrimeQ[c]&&n>b&&PrimeQ[n], AppendTo[lst, n]; a=b; b=n], {n, 0, 8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)
nxt[{a_, b_}]:=Module[{p=NextPrime[b]}, While[!PrimeQ[a+b+p], p= NextPrime[ p]]; {b, p}]; Transpose[NestList[nxt, {3, 5}, 70]][[1]] (* Harvey P. Dale, Aug 05 2013 *)

Prog

(PARI) { n=a1=0; forprime (p=3, 5*10^5, if (p<6 || isprime(p + s), write("b062391.txt", n++, " ", p); s=a1 + p; a1=p; if (n==1000, break)) ) } \\ Harry J. Smith, Aug 07 2009

Crossrefs

Cf. A072536, A072537, A000040.

Cf. A072225.

Sequence in context: A130097 A020612 A072539 * A038951 A020578 A250481

Adjacent sequences: A062388 A062389 A062390 * A062392 A062393 A062394

Keyword

nonn,easy

Author

Amarnath Murthy, Jun 27 2001

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jul 02 2001

Status

approved