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A174947 Triangle read by rows: T(n,k) = (prime(n)+1) mod prime(k).

%I A174947 #19 Apr 12 2024 17:42:53
%S A174947 1,0,1,0,0,1,0,2,3,1,0,0,2,5,1,0,2,4,0,3,1,0,0,3,4,7,5,1,0,2,0,6,9,7,
%T A174947 3,1,0,0,4,3,2,11,7,5,1,0,0,0,2,8,4,13,11,7,1,0,2,2,4,10,6,15,13,9,3,
%U A174947 1,0,2,3,3,5,12,4,0,15,9,7,1,0,0,2,0,9,3,8,4,19,13,11,5,1,0,2,4,2,0,5,10,6,21,15,13,7,3,1
%N A174947 Triangle read by rows: T(n,k) = (prime(n)+1) mod prime(k).
%C A174947 Triangle read by rows: T(n,k) = Sigma(prime(n)) mod prime(k), where Sigma(prime(.)) is the sum of divisors of prime.
%H A174947 G. C. Greubel, <a href="/A174947/b174947.txt">Rows n = 1..50 of the triangle, flattened</a>
%e A174947 Triangle begins
%e A174947   1;
%e A174947   0, 1;
%e A174947   0, 0, 1;
%e A174947   0, 2, 3, 1;
%e A174947   0, 0, 2, 5, 1;
%e A174947   0, 2, 4, 0, 3,  1;
%e A174947   0, 0, 3, 4, 7,  5,  1;
%e A174947   0, 2, 0, 6, 9,  7,  3,  1;
%e A174947   0, 0, 4, 3, 2, 11,  7,  5, 1;
%e A174947   0, 0, 0, 2, 8,  4, 13, 11, 7, 1;
%t A174947 Table[Mod[1+Prime[n], Prime[k]], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Apr 10 2024 *)
%o A174947 (PARI) trga(nrows) = {for (n=1, nrows, for (k=1, n, print1(sigma(prime(n)) % prime(k), ", ");); print(););} \\ _Michel Marcus_, Apr 11 2013
%o A174947 (Magma)
%o A174947 [(1+NthPrime(n)) mod NthPrime(k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Apr 10 2024
%o A174947 (SageMath)
%o A174947 flatten([[(1+nth_prime(n))%nth_prime(k) for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Apr 10 2024
%Y A174947 Cf. A174428, A173655, A173662, A174996, A175620, A177226.
%K A174947 nonn,tabl
%O A174947 1,8
%A A174947 _Juri-Stepan Gerasimov_, Dec 02 2010
%E A174947 Corrected by _D. S. McNeil_, Dec 02 2010