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Primes of the form 8*k-1 such that 4*k-1, 16*k-1 and 32*k-1 are also primes.
7

%I #8 May 13 2024 02:14:39

%S 359,719,5399,7079,24239,34319,54959,107279,115679,126839,142799,

%T 149399,164999,175079,202799,214559,215399,225839,244199,245639,

%U 253679,254279,266999,278879,333479,335519,459479,507359,508559

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

%H Amiram Eldar, <a href="/A101796/b101796.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 8*A101794(n) - 1 = 2*A101795(n) + 1. - _Amiram Eldar_, May 13 2024

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

%t 8 * Select[Range[10^5], And @@ PrimeQ[2^Range[2, 5]*# - 1] &] - 1 (* _Amiram Eldar_, May 13 2024 *)

%o (PARI) is(k) = if(k % 8 == 7, my(m = k\8 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1) && isprime(32*m-1), 0); \\ _Amiram Eldar_, May 13 2024

%Y Cf. A002515, A101794, A101795, A101797, A101798.

%Y Subsequence of A007522 and A101792.

%Y Subsequence: A101996.

%K easy,nonn

%O 1,1

%A Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004