|
%I #30 Feb 21 2024 01:46:19
%S 1,4,7,9,10,13,14,16,19,21,22,24,25,28,29,31,34,35,37,39,40,42,43,44,
%T 46,49,52,54,55,56,57,58,59,61,63,64,67,68,69,70,73,74,76,77,79,81,82,
%U 84,85,88,89,90,91,94,97,98,99,100,101,103,104,105,106,107,109,112,114,115
%N Numbers n such that 2*n + 7 is not a prime.
%C Let p = prime number, n = (p^2-7)/2 (mod p).
%C Comment: All numbers of the form 1+3k (k=0,1,2,...) are in this sequence, since 2(3k+1)+7 = 6k+9 is divisible by 3. Moreover, each of these numbers can be extended to an equidistant sequence of length k+1 and step 2k+3: This leads to the triangle T[k,m] = (3k+1)+(2k+3)*m, m=0,...,k, of elements of this sequence, because T[k,m]*2+7 = (2k+3)(2m+3) is never prime. The lines of the triangle end with m=k since the next term T[k,k+1] would be the same as the term in the following line, T[k+1,k]. (The formula T[k,m]=((2k+3)(2m+3)-7)/2 might also explain the comment involving "n=(p^2-7)/2".) [_M. F. Hasler_, Jun 16 2010]
%H Vincenzo Librandi, <a href="/A153053/b153053.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Range[200], !PrimeQ[2# + 7] &] (* _Vincenzo Librandi_, Nov 21 2012 *)
%o (PARI) for(n=1,200,isprime(2*n+7)||print1(n", ")) \\ _M. F. Hasler_, Jun 16 2010
%o (Magma) [n: n in [1..120] | not IsPrime(2*n + 7)]; // _Vincenzo Librandi_, Nov 21 2012
%Y Cf. A105760, A154684.
%K nonn,easy
%O 1,2
%A _Vincenzo Librandi_, Dec 17 2008
%E Checked and extended by _M. F. Hasler_, Jun 16 2010
|
