A281937 Numbers k such that k - 13, k + 1, k + 5, k + 7, and k + 13 are all prime.

66, 96, 1446, 2706, 7206, 9336, 11826, 19416, 21516, 28656, 42696, 52176, 71706, 79146, 81546, 88806, 126486, 136986, 140676, 151896, 159786, 167436, 188856, 222786, 223836, 245976, 266676, 272346, 284736, 330426, 340926, 349926, 375246, 375996, 389526, 395106

Offset

1,1

Comments

Consider 4 distinct numbers a, b, c, d such that all 5 numbers a+b+c+d, -a+b+c+d, a-b+c+d, a+b-c+d and a+b+c-d are positive/negative primes. The sequence give values of d for fixed values a=3, b=4, c=6.

Apparently a=3, b=4, c=6 is the least possible set.

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Mathematica

Reap[Do[If[PrimeQ[a + b - c + d] && PrimeQ[a - b + c + d] && PrimeQ[-a + b + c + d] && PrimeQ[a + b + c - d] && PrimeQ[a + b + c + d], Sow[d]], {a, 3, 3}, {b, 4, 4}, {c, 6, 6}, {d, 1 + c, 100000}]][[2, 1]]
fQ[n_] := Times @@ Boole@ PrimeQ[{n +13, n +7, n +5, n +1, n -13}] == 1; Select[6 + 30*Range[2, 13100], fQ] (* Robert G. Wilson v, Feb 03 2017 *)

Prog

(PARI) is(n)=isprime(n-13) && isprime(n+1) && isprime(n+5) && isprime(n+7) && isprime(n+13) \\ Charles R Greathouse IV, Feb 06 2017

Crossrefs

Sequence in context: A098775 A109759 A194196 * A109141 A350197 A350204

Adjacent sequences: A281934 A281935 A281936 * A281938 A281939 A281940

Keyword

nonn

Author

Zak Seidov, Feb 02 2017

Extensions

New NAME from Charles R Greathouse IV, Feb 06 2017

Status

approved