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%I #25 Jul 18 2023 02:07:53
%S 3,9,24,27,48,57,69,78,87,99,114,153,168,189,192,213,219,234,252,273,
%T 303,324,357,372,387,399,402,423,468,498,534,567,573,594,597,609,618,
%U 654,672,687,699,708,714,738,759,804,813,864,882,903,918,924,948,969,1032,1038,1128,1182,1197,1203,1233,1242,1269,1308,1353
%N Numbers k such that 4k+1 and 4(k+1)+1 are primes.
%C Both k and k+1 are terms in A005098. All terms are multiples of 3.
%C 4k+1 and 4(k+1)+1 are pairs of consecutive primes. Notice that in all cases, the numbers 4(k-1)+1 and 4(k+2)+1 are not prime as they are multiples of 3.
%H Seiichi Manyama, <a href="/A254010/b254010.txt">Table of n, a(n) for n = 1..10000</a>
%p A254010:=n->`if`(isprime(4*n+1) and isprime(4*(n+1)+1), n, NULL): seq(A254010(n), n=1..2000); # _Wesley Ivan Hurt_, Apr 23 2015
%t Select[Range[1000], PrimeQ[4 # + 1] && PrimeQ[4 (# + 1) + 1] &] (* _Vincenzo Librandi_, Apr 24 2015 *)
%o (Magma) [n: n in [0..1000] | IsPrime(4*n+1) and IsPrime(4*(n+1)+1)]; // _Vincenzo Librandi_, Apr 24 2015
%Y Cf. A005098.
%K nonn
%O 1,1
%A _Zak Seidov_, Jan 22 2015