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
Examples
After 43, the next term is 53, since 31 + 43 + 47 = 121 is not prime and 31 + 43 + 53 = 127 is prime.
Links
- Zak Seidov, Table of n, a(n) for n = 1..1000.
Programs
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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 *) -
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
Extensions
Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jul 02 2001
Comments