A085053 Number of primes of the form nk+1, where k=1 to n; 0 if no such number exists.

1, 2, 1, 3, 1, 5, 2, 2, 3, 6, 3, 6, 4, 6, 5, 6, 3, 10, 2, 7, 6, 9, 4, 10, 5, 10, 7, 11, 4, 17, 3, 10, 9, 12, 9, 16, 4, 9, 11, 14, 5, 21, 7, 11, 10, 16, 8, 19, 6, 18, 13, 17, 5, 24, 10, 19, 9, 16, 8, 27, 7, 15, 13, 16, 13, 30, 9, 18, 13, 27, 9, 26, 10, 20, 18, 17, 11, 29, 11, 23, 18, 22, 11

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 26 2003

Keywords

• nonn

Comments

Conjecture: no entry is zero; i.e. for every n there exists a prime of the form nk+1, k<=n.

The conjecture is essentially the same as the one in A034693, which has a long history in the study of primes in arithmetic progression. - T. D. Noe, Jun 29 2003

Examples

			When formatted as an array of primes of the form nk+1 up to n^2+1:
2
3,5
7
5,13,17
11
7,13,19,31,37
29,43
17,41
19,37,73
11,31,41,61,71,101
23,67,89
13,37,61,73,97,109
53,79,131,157
29,43,71,113,127,197
The sequence contains the number of terms in the n-th row.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A034693 (smallest k such that kn+1 is prime).

Programs

Mathematica

Table[cnt=0; Do[If[PrimeQ[k*n+1], cnt++ ], {k, n}]; cnt, {n, 100}]
Table[Count[n*Range[n]+1,?PrimeQ],{n,90}] (* _Harvey P. Dale, Jan 24 2014 *)

PARI

a(m)=local(c); for(n=1,m,c=0; for(k=1,n,if(isprime(n*k+1),c++; )); print1(c","))

Extensions

Edited, corrected and extended by T. D. Noe, Ray Chandler and Jason Earls, Jun 28 2003