A101995 - OEIS

%I #7 May 13 2024 02:14:20

%S 179,53639,63419,126839,127139,254279,296099,340919,607319,810539,

%T 1069199,1122659,1598699,1621619,1820999,1866239,1912679,1920959,

%U 2045339,2138399,2157899,2245319,2278079,2357219,2667779,2865839

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

%H Amiram Eldar, <a href="/A101995/b101995.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 4*A101994(n) - 1. - _Amiram Eldar_, May 13 2024

%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 179 is a term.

%t 4 * Select[Range[10^5], And @@ PrimeQ[2^Range[2, 6]*# - 1] &] - 1 (* _Amiram Eldar_, May 13 2024 *)

%o (PARI) is(k) = if(k % 4 == 3, my(m = k\4 + 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 Cf. A002515, A101794.

%Y Cf. A101994, A101996, A101997, A101998, A101999.

%Y Subsequence of A002145, A101791 and A101795.

%K easy,nonn

%O 1,1

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