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A269354
Numbers k such that 10k - 3, 10k - 1, 10k + 1 and 10k + 3 are divisible only by primes congruent to 3 mod 4.
1
8, 13, 21, 44, 50, 75, 89, 99, 133, 146, 150, 245, 254, 289, 319, 327, 395, 468, 500, 517, 579, 601, 608, 691, 704, 761, 764, 878, 1011, 1098, 1125, 1199, 1266, 1298, 1313, 1315, 1414, 1495, 1544, 1716, 1723, 1752, 1762, 1781, 1844, 2043, 2073, 2186, 2281, 2291, 2309, 2360, 2444, 2455, 2457
OFFSET
1,1
COMMENTS
Prime terms: 13, 89, 601, 691, 761, 1723, 2281, 2309, 2693, 5437, 5821, 6199, ...
LINKS
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
Cf. A004614.
Sequence in context: A063849 A273980 A101642 * A195984 A019535 A229446
KEYWORD
nonn,easy
AUTHOR
STATUS
approved