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A101798 Primes of the form 32*k-1 such that 4*k-1, 8*k-1 and 16*k-1 are also primes.

%I A101798 #10 Feb 20 2025 13:51:57
%S A101798 1439,2879,21599,28319,96959,137279,219839,429119,462719,507359,
%T A101798 571199,597599,659999,700319,811199,858239,861599,903359,976799,
%U A101798 982559,1014719,1017119,1067999,1115519,1333919,1342079,1837919,2029439,2034239
%N A101798 Primes of the form 32*k-1 such that 4*k-1, 8*k-1 and 16*k-1 are also primes.
%H A101798 Amiram Eldar, <a href="/A101798/b101798.txt">Table of n, a(n) for n = 1..10000</a>
%F A101798 a(n) = 32*A101794(n) - 1 = 8*A101795(n) + 7 = 4*A101796(n) + 3 = 2*A101797(n) + 1. - _Amiram Eldar_, May 13 2024
%e A101798 4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719 and 32*45-1 = 1439 are primes, so 1439 is a term.
%t A101798 32 * Select[Range[10^5], And @@ PrimeQ[2^Range[2, 5]*# - 1] &] - 1 (* _Amiram Eldar_, May 13 2024 *)
%t A101798 Select[Prime[Range[200000]],Mod[#,32]==31&&AllTrue[{4,8,16} (#+1)/32-1,PrimeQ]&] (* _Harvey P. Dale_, Feb 20 2025 *)
%o A101798 (PARI) is(k) = if(k % 32 == 31, my(m = k\32 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1) && isprime(32*m-1), 0); \\ _Amiram Eldar_, May 13 2024
%Y A101798 Cf. A002515, A101794, A101795, A101796, A101797.
%Y A101798 Subsequence of A127578.
%Y A101798 Subsequence: A101998.
%K A101798 easy,nonn
%O A101798 1,1
%A A101798 Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004