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Triangle of n-th prime modulo twice primes less n-th prime.
4

%I #10 Sep 28 2017 05:41:31

%S 2,3,3,1,5,5,3,1,7,7,3,5,1,11,11,1,1,3,13,13,13,1,5,7,3,17,17,17,3,1,

%T 9,5,19,19,19,19,3,5,3,9,1,23,23,23,23,1,5,9,1,7,3,29,29,29,29,3,1,1,

%U 3,9,5,31,31,31,31,31,1,1,7,9,15,11,3,37,37,37,37,37,1,5,1,13,19,15,7,3,41

%N Triangle of n-th prime modulo twice primes less n-th prime.

%C The right border of the triangle are the primes: T(n,n)=A000040(n); T(n,1)=A039702(n), T(n,2)=A039704(n) for n>1, T(n,3)=A007652(n) for n>2, T(n,4)=A039712(n) for n>3;

%F T(n, k) = prime(n) mod 2*prime(k), 1<=k<=n.

%e Triangle begins:

%e 2;

%e 3, 3;

%e 1, 5, 5;

%e 3, 1, 7, 7;

%e 3, 5, 1, 11, 11;

%e 1, 1, 3, 13, 13, 13;

%e 1, 5, 7, 3, 17, 17, 17;

%e ...

%p A079950 := proc(n,k)

%p modp(ithprime(n),2*ithprime(k)) ;

%p end proc:

%p seq(seq(A079950(n,k),k=1..n),n=1..12) ; # _R. J. Mathar_, Sep 28 2017

%o (PARI) T(n,k) = prime(n) % (2*prime(k));

%o tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, Sep 21 2017

%Y Cf. A001747, A079951, A079952, A079953.

%K nonn,tabl

%O 1,1

%A _Reinhard Zumkeller_, Jan 19 2003