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.

3, 5, 11, 13, 29, 31, 43, 83, 97, 113, 127, 149, 157, 173, 191, 193, 223, 311, 373, 467, 487, 499, 557, 607, 647, 653, 673, 677, 739, 787, 821, 829, 881, 883, 977, 991, 1051, 1217, 1291, 1373, 1427, 1429, 1471, 1583, 1597, 1607, 1609, 1693, 1811, 1877, 1951

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 17 2008, corrected Dec 19 2008

Keywords

• nonn

Links

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

Crossrefs

Cf. A153065, A062391.

Programs

Maple

A:= 3,5,11,13:
for n from 1 to 100 do
  s:= A[-1]+A[-2];
  t:= s + A[-3]+A[-4];
  for x from A[-1]+2 by 2 while not(isprime(x)) or not(isprime(x+s)) or not(isprime(x+t)) do od:
  A:= A, x;
od:
A; # Robert Israel, Mar 09 2017

Mathematica

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 *)