A182121 Primes p such that the sum of both three and five consecutive primes starting with p is prime.

5, 7, 11, 19, 29, 31, 53, 67, 79, 109, 149, 157, 163, 211, 229, 311, 349, 379, 401, 409, 449, 467, 653, 757, 809, 839, 857, 863, 883, 983, 997, 1033, 1087, 1103, 1187, 1193, 1289, 1301, 1303, 1409, 1481, 1523, 1553, 1637, 1663, 1669, 1709, 1951, 1973

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

5 is in the sequence because 5 + 7 + 11 = 23 is prime and 5 + 7 + 11 + 13 + 17 = 53 is also prime.

Mathematica

cpQ[n_]:=Module[{ppi=PrimePi[n], cnsc}, cnsc=Prime[Range[ppi, ppi+4]]; And@@ PrimeQ[ {Total[cnsc], Total[Take[cnsc, 3]]}]]; Select[Prime[Range[300]], cpQ] (* Harvey P. Dale, Mar 28 2013 *)
Select[Partition[Prime[Range[500]], 5, 1], AllTrue[{Total[Take[#, 3]], Total[#]}, PrimeQ]&][[;; , 1]] (* Harvey P. Dale, Feb 11 2024 *)

Prog

(PARI) {a=2; b=3; c=5; d=7; e=11; for(n=1, 300, s=a+b+c+d+e;
if(isprime(s)&&isprime(a+b+c), print1(a", ")); a=b; b=c; c=d; d=e; e=nextprime(e+2))}

Crossrefs

Intersection of A073681 and A152468.

Sequence in context: A040127 A341215 A136086 * A072825 A045440 A023235

Adjacent sequences: A182118 A182119 A182120 * A182122 A182123 A182124

Keyword

nonn

Author

Zak Seidov, Dec 17 2012

Status

approved