A154497 a(n) is the least prime > a(n-1) such that a(n-2) + a(n-1) + a(n) is prime, with a(1)=3, a(2)=11.

3, 11, 17, 19, 23, 29, 31, 37, 41, 53, 73, 97, 101, 109, 127, 131, 139, 149, 151, 157, 179, 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, 967, 983, 1013, 1087

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Keywords

• nonn

Examples

			3+11+17 = 31, 11+17+19 = 47, 17+19+23 = 59, ...
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495, A154496, A062391.

Programs

Maple

A[1]:= 3: A[2]:= 11:
for i from 3 to 100 do
  p:= A[i-1];
  do
    p:= nextprime(p);
    if isprime(A[i-2]+A[i-1]+p) then
       A[i]:= p; break
    fi
  od
od:
seq(A[i],i=1..100); # Robert Israel, Jan 17 2023

Mathematica

a=3;b=11;lst={a,b};Do[c=Prime[n];p=a+b+c;If[PrimeQ[p],AppendTo[lst,c];a=b;b=c],{n,5,6!}];lst

Extensions

NAME adapted to offset by R. J. Mathar, Jun 19 2021

Name corrected by Robert Israel, Jan 17 2023