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A101998 Primes of the form 32*k-1 such that 4*k-1, 8*k-1, 16*k-1 and 64*k-1 are also primes.

%I A101998 #8 May 13 2024 02:14:11
%S A101998 1439,429119,507359,1014719,1017119,2034239,2368799,2727359,4858559,
%T A101998 6484319,8553599,8981279,12789599,12972959,14567999,14929919,15301439,
%U A101998 15367679,16362719,17107199,17263199,17962559,18224639,18857759
%N A101998 Primes of the form 32*k-1 such that 4*k-1, 8*k-1, 16*k-1 and 64*k-1 are also primes.
%H A101998 Amiram Eldar, <a href="/A101998/b101998.txt">Table of n, a(n) for n = 1..10000</a>
%F A101998 a(n) = 32*A101994(n) - 1 = 8*A101995(n) + 7 =  4*A101996(n) + 3 = 2*A101997(n) + 1. - _Amiram Eldar_, May 13 2024
%e A101998 4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719, 32*45-1 = 1439 and 64*45-1 = 2879 are primes, so 1439 is a term.
%t A101998 32 * Select[Range[10^5], And @@ PrimeQ[2^Range[2, 6]*# - 1] &] - 1 (* _Amiram Eldar_, May 13 2024 *)
%o A101998 (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) && isprime(64*m-1), 0); \\ _Amiram Eldar_, May 13 2024
%Y A101998 Cf. A101994, A101995, A101996, A101997, A101999.
%Y A101998 Subsequence of A127578 and A101798.
%K A101998 easy,nonn
%O A101998 1,1
%A A101998 Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 23 2004