OFFSET
2,6
COMMENTS
a(n) > 0 for all n > 2.
LINKS
Zhi-Wei Sun, On permutations of {1,...,n} and related topics, J. Algebraic Combin., 2021.
EXAMPLE
a(3) = 1 with p = 2^(1-1) + 1^(3-1) + 3^(2-1) = 5, p - 2 = 3 and p + 6 = 11 all prime.
a(4) = 1 with p = 1^(3-1) + 3^(2-1) + 2^(4-1) + 4^{1-1) = 13, p - 2 = 11 and p + 6 = 19 all prime.
a(5) = 1 with p = 2^(4-1) + 4^(3-1) + 3^(1-1) + 1^(5-1) + 5^(2-1) = 31, p - 2 = 29 and p + 6 = 37 all prime.
a(6) = 1 with p = 4^(3-1) + 3^(1-1) + 1^(5-1) + 5^(2-1) + 2^(6-1) + 6^(4-1) = 271, p - 2 = 269 and p + 6 = 277 all prime.
a(10) > 0 since p = 4^(8-1) + 8^(5-1) + 5^(6-1) + 6^(3-1) + 3^(9-1) + 9^(1-1) + 1^(7-1) + 7^(2-1) + 2^(10-1) + 10^(4-1) = 31723, p - 2 = 31721 and p + 6 = 31729 are all prime.
MATHEMATICA
(* A program to compute a(7): *)
PQ[n_]:=PQ[n]=PrimeQ[n]&&PrimeQ[n-2]&&PrimeQ[n+6];
V[i_]:=V[i]=Part[Permutations[{1, 2, 3, 4, 5, 6}], i];
S[i_]:=S[i]=Sum[V[i][[j]]^(V[i][[j+1]]-1), {j, 1, 5}]+V[i][[6]]^6+7^(V[i][[1]]-1);
n=0; Do[If[PQ[S[i]], n=n+1], {i, 1, 6!}]; Print[7, " ", n]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Zhi-Wei Sun, Apr 01 2021
EXTENSIONS
a(11)-a(13) from Jinyuan Wang, Apr 02 2021
STATUS
approved