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

1,2

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A173238 A173284 A278136 * A296118 A296121 A277120

Adjacent sequences: A085050 A085051 A085052 * A085054 A085055 A085056

Keyword

nonn

Author

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

Extensions

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

Status

approved