A288107 Numbers k such that p = prime(k) + prime(k+1) + prime(k+2), q = p + prime(k+3) + prime(k+4) and r = q + prime(k+5) + prime(k+6) are all prime.

8, 10, 11, 16, 22, 75, 79, 146, 153, 212, 223, 297, 298, 319, 389, 406, 411, 479, 505, 527, 531, 603, 640, 650, 739, 765, 800, 824, 918, 925, 978, 1063, 1137, 1241, 1319, 1368, 1468, 1566, 1648, 1667, 1737, 1779, 1828, 1877, 1972, 1977, 2075, 2302, 2387, 2425, 2442, 2476, 2886

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Mathematica

With[{nn = 4100}, Function[s, Select[Range[nn - 6], Block[{p, q, r}, r = Total@ {Set[q, Total@ {Set[p, Total@ {#1, #2, #3}], #4, #5}], #6, #7}; AllTrue[{p, q, r}, PrimeQ]] & @@ Take[s, {#, # + 6}] &]]@ Prime@ Range@ nn] (* Michael De Vlieger, Jun 06 2017, Version 10 *)
apQ[{a_, b_, c_, d_, e_, f_, g_}]:=Module[{p1=a+b+c, p2}, p2=p1+d+e; AllTrue[ {p1, p2, p2+f+g}, PrimeQ]]; PrimePi/@Select[Partition[Prime[Range[3000]], 7, 1], apQ][[;; , 1]] (* Harvey P. Dale, Apr 21 2023 *)

Prog

(PARI) list(lim)=my(v=List(), u=primes(7), n=1, p, q); forprime(s=u[7]+1, , if(n++>lim, break); u=concat(u[2..7], s); if(isprime(p=u[1]+u[2]+u[3]) && isprime(q=p+u[4]+u[5]) && isprime(q+u[6]+u[7]), listput(v, n))); Vec(v) \\ Charles R Greathouse IV, Jun 07 2017

Crossrefs

Sequence in context: A256385 A274560 A122990 * A062372 A046031 A102758

Adjacent sequences: A288104 A288105 A288106 * A288108 A288109 A288110

Keyword

nonn

Author

Zak Seidov, Jun 05 2017

Status

approved