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A174996 Triangle read by rows: T(n,k) = (prime(n)-1) mod prime(k).

%I A174996 #19 Apr 13 2024 05:03:51
%S A174996 1,0,2,0,1,4,0,0,1,6,0,1,0,3,10,0,0,2,5,1,12,0,1,1,2,5,3,16,0,0,3,4,7,
%T A174996 5,1,18,0,1,2,1,0,9,5,3,22,0,1,3,0,6,2,11,9,5,28,0,0,0,2,8,4,13,11,7,
%U A174996 1,30,0,0,1,1,3,10,2,17,13,7,5,36,0,1,0,5,7,1,6,2,17,11,9,3,40,0,0,2,0,9,3,8,4,19,13,11,5,1,42
%N A174996 Triangle read by rows: T(n,k) = (prime(n)-1) mod prime(k).
%H A174996 G. C. Greubel, <a href="/A174996/b174996.txt">Rows n = 1..50 of the triangle, flattened</a>
%e A174996 The triangle starts in row n=0 with columns 1<=k<= n as:
%e A174996   1;
%e A174996   0, 2;
%e A174996   0, 1, 4;
%e A174996   0, 0, 1, 6;
%e A174996   0, 1, 0, 3, 10;
%e A174996   0, 0, 2, 5,  1, 12;
%e A174996   0, 1, 1, 2,  5,  3, 16;
%e A174996   0, 0, 3, 4,  7,  5,  1, 18;
%e A174996   0, 1, 2, 1,  0,  9,  5,  3, 22;
%e A174996   0, 1, 3, 0,  6,  2, 11,  9,  5, 28;
%t A174996 Flatten[Table[Mod[Prime[n]-1,Prime[k]],{n,15},{k,n}]]  (* _Harvey P. Dale_, Apr 23 2011 *)
%o A174996 (Magma)
%o A174996 [(NthPrime(n)-1) mod NthPrime(k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Apr 12 2024
%o A174996 (SageMath)
%o A174996 flatten([[(nth_prime(n)-1)%nth_prime(k) for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Apr 12 2024
%Y A174996 Cf. A006093, A173655, A173662, A174428, A174947, A175620, A176066, A177226.
%K A174996 nonn,tabl
%O A174996 1,3
%A A174996 _Juri-Stepan Gerasimov_, Dec 02 2010