OFFSET
1,1
COMMENTS
It has been proved in the reference that for every prime p there exists a prime of the form k*p+1. Conjecture: sequence is infinite, i.e., for every n there exists a prime of the form n*k+1 (cf. A034693).
Both follow directly from Dirichlet's theorem. [Charles R Greathouse IV, Feb 28 2012]
REFERENCES
Amarnath Murthy, On the divisors of Smarandache Unary Sequence. Smarandache Notions Journal, Vol. 11, 2000.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..591
EXAMPLE
The first few rows of the triangle are
2
3 7
7 29 59
5 11 23 47
11 23 47 283 1699
7 29 59 709 2837 22697
MATHEMATICA
f[1]=2; f[n_] := f[n] = Block[{p=2}, While[Mod[p, n] != 1, p = NextPrime[p]]; p];
Flatten[Table[Rest @ NestList[f, j, j], {j, 9}]]
(* Jean-François Alcover, May 31 2011, improved by Robert G. Wilson v *)
PROG
(PARI 2.1.3) for(j=1, 9, q=j; for(k=1, j, m=1; while(!isprime(p=m*q+1, 1), m++); print1(q=p, ", ")))
(PARI) f(n)=my(k=n+1); while(!isprime(k), k+=n); k
T(j, k)=for(i=1, k, j=f(j)); j \\ Charles R Greathouse IV, Feb 28 2012
(Magma) f:=function(n) m:=1; while not IsPrime(m*n+1) do m+:=1; end while; return m*n+1; end function; &cat[ [ k eq 1 select f(j) else f(Self(k-1)): k in [1..j] ]: j in [1..9] ]; // Klaus Brockhaus, May 30 2009
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Amarnath Murthy, May 08 2003
EXTENSIONS
Edited, corrected and extended by Klaus Brockhaus, May 13 2003
STATUS
approved