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A085053 Number of primes of the form nk+1, where k=1 to n; 0 if no such number exists. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 14 14:21 EDT 2021. Contains 345025 sequences. (Running on oeis4.)