A101793 - OEIS

%I #16 May 13 2024 02:14:59

%S 47,719,1439,2879,4079,4127,5807,6047,7247,7727,9839,10799,11279,

%T 13967,14159,15647,21599,24527,28319,28607,42767,44687,45887,48479,

%U 51599,51839,67247,68639,72767,77279,79967,81647,84047,84719,89087,92399,95279,96959,98207

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

%H Amiram Eldar, <a href="/A101793/b101793.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 16*A101790(n) - 1 = 4*A101791(n) + 3 = 2*A101792(n) + 1. - _Amiram Eldar_, May 13 2024

%e 4*3-1 = 11, 8*3-1 = 23 and 16*3-1 = 47 are primes, so 47 is a term.

%t 16#-1&/@Select[Range[10000],AllTrue[{4#-1,8#-1,16#-1},PrimeQ]&] (* _Harvey P. Dale_, Jun 13 2015 *)

%o (PARI) is(k) = if(k % 16 == 15, my(m = k\16 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1), 0); \\ _Amiram Eldar_, May 13 2024

%Y Cf. A002515, A101790, A101791, A101792.

%Y Subsequence of A127576.

%Y Subsequences: A101797, A101997.

%K easy,nonn

%O 1,1

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