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A101791 Primes of the form 4*k-1 such that 8*k-1 and 16*k-1 are also primes.

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%I A101791 #14 May 13 2024 02:15:06
%S A101791 11,179,359,719,1019,1031,1451,1511,1811,1931,2459,2699,2819,3491,
%T A101791 3539,3911,5399,6131,7079,7151,10691,11171,11471,12119,12899,12959,
%U A101791 16811,17159,18191,19319,19991,20411,21011,21179,22271,23099,23819
%N A101791 Primes of the form 4*k-1 such that 8*k-1 and 16*k-1 are also primes.
%H A101791 Amiram Eldar, <a href="/A101791/b101791.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%F A101791 a(n) = 4*A101790(n) - 1. - _Amiram Eldar_, May 13 2024
%e A101791 4*3-1 = 11, 8*3-1 = 23 and 16*3-1 = 47 are primes, so 11 is a term.
%t A101791 p4816Q[n_]:=Module[{nn=(n+1)/4},And@@PrimeQ[{n,8nn-1,16nn-1}]]; Select[ 4*Range[6000]-1,p4816Q] (* _Harvey P. Dale_, Nov 25 2011 *)
%o A101791 (PARI) is(k) = if(k % 4 == 3, my(m = k\4 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1), 0); \\ _Amiram Eldar_, May 13 2024
%Y A101791 Cf. A002515, A101790, A101792, A101793.
%Y A101791 Subsequence of A002145.
%Y A101791 Subsequences: A101795, A101995.
%K A101791 easy,nonn
%O A101791 1,1
%A A101791 Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004