A153053 Numbers j such that 2*j + 7 is not a prime.

1, 4, 7, 9, 10, 13, 14, 16, 19, 21, 22, 24, 25, 28, 29, 31, 34, 35, 37, 39, 40, 42, 43, 44, 46, 49, 52, 54, 55, 56, 57, 58, 59, 61, 63, 64, 67, 68, 69, 70, 73, 74, 76, 77, 79, 81, 82, 84, 85, 88, 89, 90, 91, 94, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 109, 112, 114, 115

Offset: 1

Author

Vincenzo Librandi, Dec 17 2008

Keywords

• nonn
• easy

Comments

Let p = prime number, n = (p^2-7)/2 (mod p).

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]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A105760, A154684.

Programs

Magma

[n: n in [1..120] | not IsPrime(2*n + 7)]; // Vincenzo Librandi, Nov 21 2012

Mathematica

Select[Range[200], !PrimeQ[2# + 7] &] (* Vincenzo Librandi, Nov 21 2012 *)

PARI

for(n=1,200,isprime(2*n+7)||print1(n", ")) \\ M. F. Hasler, Jun 16 2010

Extensions

Checked and extended by M. F. Hasler, Jun 16 2010