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%I #15 Sep 08 2022 08:46:06
%S 2,7,13,19,29,37,53,71,101,107,131,139,163,173,181,199,223,229,263,
%T 281,293,311,337,397,443,463,491,557,569,659,673,719,733,787,809,827,
%U 839,857,953,983,1013,1069,1091,1109,1151,1223,1249,1283,1307,1451,1493,1549
%N Primes p such that p + 3*k is also prime, where p is k-th prime.
%H K. D. Bajpai, <a href="/A231383/b231383.txt">Table of n, a(n) for n = 1..5100</a>
%e a(5)= 29 which is 10th prime. prime(10)+3*10= 29+30= 59 which is also prime.
%e a(7)= 53 which is 16th prime. prime(16)+3*16= 53+48= 101 which is also prime.
%p KD := proc() local a, b; a:= ithprime(n); b:= a+3*n; if isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..500);
%t KD = Select[Table[{Prime[n], Prime[n] + 3*n}, {n, 200}], PrimeQ[#[[2]]] &]; Transpose[KD][[1]]
%o (PARI) is(n)=isprime(n) && isprime(n+3*primepi(n)) \\ _Charles R Greathouse IV_, Nov 08 2013
%o (Magma) [NthPrime(n): n in [1..250] | IsPrime(NthPrime(n)+3*n)]; // _Vincenzo Librandi_, Jan 19 2015
%Y Cf. A061068 (primes: prime(m) plus its subscript).
%Y Cf. A064402 (numbers n: prime(n)+n is prime).
%Y Cf. A231232 (primes p : p+2*k is also prime).
%K nonn
%O 1,1
%A _K. D. Bajpai_, Nov 08 2013
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