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%I #12 May 13 2024 02:14:35
%S 719,1439,10799,14159,48479,68639,109919,214559,231359,253679,285599,
%T 298799,329999,350159,405599,429119,430799,451679,488399,491279,
%U 507359,508559,533999,557759,666959,671039,918959,1014719,1017119,1148879
%N Primes of the form 16*k-1 such that 4*k-1, 8*k-1 and 32*k-1 are also primes.
%H Amiram Eldar, <a href="/A101797/b101797.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%F a(n) = 16*A101794(n) - 1 = 4*A101795(n) + 3 = 2*A101796(n) + 1. - _Amiram Eldar_, May 13 2024
%e 4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719 and 32*45-1 = 1439 are primes, so 719 is a term.
%t 16#-1&/@Select[Range[80000],AllTrue[#*2^Range[2,5]-1,PrimeQ]&] (* _Harvey P. Dale_, Apr 25 2015 *)
%o (PARI) is(k) = if(k % 16 == 15, my(m = k\16 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1) && isprime(32*m-1), 0); \\ _Amiram Eldar_, May 13 2024
%Y Cf. A002515, A101794, A101795, A101796, A101798.
%Y Subsequence of A127576 and A101793.
%Y Subsequence: A101997.
%K easy,nonn
%O 1,1
%A Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004