login
Numbers k such that 4*k-1, 8*k-1, 16*k-1, 32*k-1 and 64*k-1 are all primes.
10

%I #9 May 13 2024 02:14:25

%S 45,13410,15855,31710,31785,63570,74025,85230,151830,202635,267300,

%T 280665,399675,405405,455250,466560,478170,480240,511335,534600,

%U 539475,561330,569520,589305,666945,716460,743160,748215,766785,799350,860835

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

%H Amiram Eldar, <a href="/A101994/b101994.txt">Table of n, a(n) for n = 1..10000</a>

%e 4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719, 32*45-1 = 1439 and 64*45-1 = 2879 are primes, so 45 is a term.

%t Select[Range[10^6], And @@ PrimeQ[2^Range[2, 6]*# - 1] &] (* _Amiram Eldar_, May 13 2024 *)

%o (PARI) is(k) = isprime(4*k-1) && isprime(8*k-1) && isprime(16*k-1) && isprime(32*k-1) && isprime(64*k-1); \\ _Amiram Eldar_, May 13 2024

%Y Cf. A002515, A101995, A101996, A101997, A101998, A101999.

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

%K easy,nonn

%O 1,1

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