OFFSET
1,1
COMMENTS
Prime terms: 13, 89, 601, 691, 761, 1723, 2281, 2309, 2693, 5437, 5821, 6199, ...
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
EXAMPLE
8 is a term because 10*8 - 3 = 77 = 7*11, 10*8 - 1 = 79, 10*8 + 1 = 81 = 3^4 and 10*8 + 3 = 83 are divisible only by primes congruent to 3 mod 4.
MAPLE
filter:= n ->
andmap(t -> numtheory:-factorset(t) mod 4 = {3}, [10*n-3, 10*n-1, 10*n+1, 10*n+3]):
select(filter, [$1..10000]); # Robert Israel, Feb 25 2016
MATHEMATICA
pc3m4Q[n_]:=AllTrue[Flatten[FactorInteger[10 n+{-3, -1, 1, 3}], 1][[All, 1]], Mod[#, 4]==3&]; Select[Range[2500], pc3m4Q] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 30 2018 *)
PROG
(Magma) [n : n in [1..3000] | forall{d: d in PrimeDivisors(10*n-3) | d mod 4 eq 3}
and forall{d: d in PrimeDivisors(10*n-1) | d mod 4 eq 3}
and forall{d: d in PrimeDivisors(10*n+1) | d mod 4 eq 3}
and forall{d: d in PrimeDivisors(10*n+3) | d mod 4 eq 3}] ;
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Juri-Stepan Gerasimov, Dec 23 2015
STATUS
approved