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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.

%I A154497 #20 Nov 29 2023 18:50:41
%S A154497 3,11,17,19,23,29,31,37,41,53,73,97,101,109,127,131,139,149,151,157,
%T A154497 179,211,223,227,233,241,269,277,281,349,353,359,379,433,467,499,521,
%U A154497 523,557,577,587,613,631,743,757,769,821,827,829,883,947,967,983,1013,1087
%N 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.
%H A154497 Robert Israel, <a href="/A154497/b154497.txt">Table of n, a(n) for n = 1..10000</a>
%e A154497 3+11+17 = 31, 11+17+19 = 47, 17+19+23 = 59, ...
%p A154497 A[1]:= 3: A[2]:= 11:
%p A154497 for i from 3 to 100 do
%p A154497   p:= A[i-1];
%p A154497   do
%p A154497     p:= nextprime(p);
%p A154497     if isprime(A[i-2]+A[i-1]+p) then
%p A154497        A[i]:= p; break
%p A154497     fi
%p A154497   od
%p A154497 od:
%p A154497 seq(A[i],i=1..100); # _Robert Israel_, Jan 17 2023
%t A154497 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
%Y A154497 Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495, A154496, A062391.
%K A154497 nonn
%O A154497 1,1
%A A154497 _Vladimir Joseph Stephan Orlovsky_, Jan 10 2009
%E A154497 NAME adapted to offset by _R. J. Mathar_, Jun 19 2021
%E A154497 Name corrected by _Robert Israel_, Jan 17 2023