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A153075 Increasing sequence of prime numbers such that the sum of any 3 consecutive terms is a prime and sum of any 5 consecutive terms is a prime also.

%I A153075 #10 Mar 09 2017 14:47:41
%S A153075 3,5,11,13,29,31,43,83,97,113,127,149,157,173,191,193,223,311,373,467,
%T A153075 487,499,557,607,647,653,673,677,739,787,821,829,881,883,977,991,1051,
%U A153075 1217,1291,1373,1427,1429,1471,1583,1597,1607,1609,1693,1811,1877,1951
%N A153075 Increasing sequence of prime numbers such that the sum of any 3 consecutive terms is a prime and sum of any 5 consecutive terms is a prime also.
%H A153075 Robert Israel, <a href="/A153075/b153075.txt">Table of n, a(n) for n = 1..10000</a>
%p A153075 A:= 3,5,11,13:
%p A153075 for n from 1 to 100 do
%p A153075   s:= A[-1]+A[-2];
%p A153075   t:= s + A[-3]+A[-4];
%p A153075   for x from A[-1]+2 by 2 while not(isprime(x)) or not(isprime(x+s)) or not(isprime(x+t)) do od:
%p A153075   A:= A, x;
%p A153075 od:
%p A153075 A; # _Robert Israel_, Mar 09 2017
%t A153075 a=3; b=5; c=11; d=13; lst={a, b, c, d}; Do[z=a+b+c+d+n; y=c+d+n; If[PrimeQ[z]&&n>b&&PrimeQ[n]&&PrimeQ[y], AppendTo[lst, n]; a=b; b=c; c=d; d=n], {n, 0, 8!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008 *)
%Y A153075 Cf. A153065, A062391.
%K A153075 nonn
%O A153075 1,1
%A A153075 _Vladimir Joseph Stephan Orlovsky_, Dec 17 2008, corrected Dec 19 2008