A288142 Numbers k such that starting with prime(k) 3, 5, 7, 9, and 11 consecutive primes sum up to prime numbers.

650, 2442, 6184, 7167, 10900, 15227, 23783, 28542, 45577, 48809, 61299, 67297, 78600, 82376, 90603, 95444, 108370, 117732, 127546, 157694, 171110, 171425, 189077, 191090, 191430, 217632, 227759, 234843, 251174, 276173, 279391, 284207, 287638, 300943, 312041

Offset

1,1

Comments

Also, numbers 6184 and 95444 are such that the sum (prime(k)+ ... + prime(k+12)) is a prime.

Links

Robert Israel, Table of n, a(n) for n = 1..105

Maple

P:= select(isprime, [seq(i, i=3..10^7, 2)]):
M:= Matrix(11, nops(P));
nP:= nops(P);
M[1, ..]:= Vector[row](P):
for i from 2 to 11 do
  M[i, 1..nP+1-i]:= M[i-1, 1..nP+1-i] + M[1, i..nP]
od:
S:= select(t -> isprime(M[3, t]) and isprime(M[5, t]) and isprime(M[7, t])
and isprime(M[9, t]) and isprime(M[11, t]), [$1..nP-11]):
map(`+`, S, 1); # Robert Israel, Jun 05 2017

Crossrefs

Sequence in context: A252538 A185666 A114047 * A157915 A158639 A162025

Adjacent sequences: A288139 A288140 A288141 * A288143 A288144 A288145

Keyword

nonn

Author

Zak Seidov, Jun 05 2017

Extensions

More terms from Robert Israel, Jun 05 2017

Status

approved