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Numbers k such that 4*k-1, 8*k-1, 16*k-1, 32*k-1, 64*k-1 and 128*k-1 are all primes.
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%I #18 May 23 2024 04:28:35

%S 15855,31785,267300,280665,399675,561330,946050,990510,1022220,

%T 1082115,1164735,1283250,1303875,1309545,1514880,1669065,1924410,

%U 2850225,3078675,3092760,3492270,3536385,3611205,3920670,4148970,4454775

%N Numbers k such that 4*k-1, 8*k-1, 16*k-1, 32*k-1, 64*k-1 and 128*k-1 are all primes.

%H Amiram Eldar, <a href="/A101320/b101320.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Iain Fox)

%e 4*15855-1, 8*15855-1, 16*15855-1, 32*15855-1, 64*15855-1 and 128*15855-1 are primes, so 15855 is a term.

%t Select[Range[10^6], And @@ PrimeQ[2^Range[2, 7]*# - 1] &] (* _Amiram Eldar_, May 23 2024 *)

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(4*n-1) && ispseudoprime(8*n-1) && ispseudoprime(16*n-1) && ispseudoprime(32*n-1) && ispseudoprime(64*n-1) && ispseudoprime(128*n-1), print1(n, ", "))) \\ _Iain Fox_, Nov 23 2017

%Y Cf. A002515.

%Y Subsequence of A005099, A005122, A101790, A101794 and A101994.

%K easy,nonn

%O 1,1

%A Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 23 2004