cp's OEIS Frontend

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

%I A085053 #18 Dec 15 2017 17:36:24
%S A085053 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,
%T A085053 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,
%U A085053 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
%N A085053 Number of primes of the form nk+1, where k=1 to n; 0 if no such number exists.
%C A085053 Conjecture: no entry is zero; i.e. for every n there exists a prime of the form nk+1, k<=n.
%C A085053 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
%H A085053 T. D. Noe, <a href="/A085053/b085053.txt">Table of n, a(n) for n = 1..5000</a>
%e A085053 When formatted as an array of primes of the form nk+1 up to n^2+1:
%e A085053 2
%e A085053 3,5
%e A085053 7
%e A085053 5,13,17
%e A085053 11
%e A085053 7,13,19,31,37
%e A085053 29,43
%e A085053 17,41
%e A085053 19,37,73
%e A085053 11,31,41,61,71,101
%e A085053 23,67,89
%e A085053 13,37,61,73,97,109
%e A085053 53,79,131,157
%e A085053 29,43,71,113,127,197
%e A085053 The sequence contains the number of terms in the n-th row.
%t A085053 Table[cnt=0; Do[If[PrimeQ[k*n+1], cnt++ ], {k, n}]; cnt, {n, 100}]
%t A085053 Table[Count[n*Range[n]+1,_?PrimeQ],{n,90}] (* _Harvey P. Dale_, Jan 24 2014 *)
%o A085053 (PARI) a(m)=local(c); for(n=1,m,c=0; for(k=1,n,if(isprime(n*k+1),c++; )); print1(c","))
%Y A085053 Cf. A034693 (smallest k such that kn+1 is prime).
%K A085053 nonn
%O A085053 1,2
%A A085053 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 26 2003
%E A085053 Edited, corrected and extended by _T. D. Noe_, _Ray Chandler_ and _Jason Earls_, Jun 28 2003