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A101999 Primes of the form 64*k-1 such that 4*k-1, 8*k-1, 16*k-1 and 32*k-1 are also primes.

%I A101999 #9 May 13 2024 02:14:07
%S A101999 2879,858239,1014719,2029439,2034239,4068479,4737599,5454719,9717119,
%T A101999 12968639,17107199,17962559,25579199,25945919,29135999,29859839,
%U A101999 30602879,30735359,32725439,34214399,34526399,35925119,36449279
%N A101999 Primes of the form 64*k-1 such that 4*k-1, 8*k-1, 16*k-1 and 32*k-1 are also primes.
%H A101999 Amiram Eldar, <a href="/A101999/b101999.txt">Table of n, a(n) for n = 1..10000</a>
%F A101999 a(n) = 64*A101994(n) - 1 = 16*A101995(n) + 15 =  8*A101996(n) + 7 = 4*A101997(n) + 3 = 2*A101998(n) + 1. - _Amiram Eldar_, May 13 2024
%e A101999 4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719, 32*45-1 = 1439 and 64*45-1 = 2879 are primes, so 2879 is a term.
%t A101999 64#-1&/@Select[Range[570000],AllTrue[#*2^Range[2,6]-1,PrimeQ]&] (* _Harvey P. Dale_, Aug 07 2021 *)
%o A101999 (PARI) is(k) = if(k % 64 == 63, my(m = k\64 + 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 A101999 Cf. A101994, A101995, A101996, A101997, A101998.
%Y A101999 Subsequence of A127579.
%K A101999 easy,nonn
%O A101999 1,1
%A A101999 Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 23 2004