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A174497 Triangle read by rows: T(n,k) = prime(n) mod (prime(n+1) - prime(k)) for 0 < k < n+1.

%I A174497 #20 Apr 10 2024 04:45:30
%S A174497 0,0,1,0,1,1,7,7,1,3,0,1,3,5,1,13,13,1,3,1,1,0,1,3,5,1,5,1,19,19,1,3,
%T A174497 7,9,1,3,23,23,23,1,5,7,11,3,5,0,1,3,5,9,11,1,5,5,1,31,31,31,1,5,7,11,
%U A174497 13,3,7,1,37,37,1,3,7,9,13,15,1,1,7,1,0,1,3,5,9,11,15,17,1,13,5,5,1
%N A174497 Triangle read by rows: T(n,k) = prime(n) mod (prime(n+1) - prime(k)) for 0 < k < n+1.
%H A174497 Michel Marcus, <a href="/A174497/b174497.txt">Rows n=1..100 of triangle, flattened</a>
%e A174497 Triangle begins as:
%e A174497    0;
%e A174497    0,  1;
%e A174497    0,  1, 1;
%e A174497    7,  7, 1, 3;
%e A174497    0,  1, 3, 5, 1;
%e A174497   13, 13, 1, 3, 1, 1;
%e A174497    0,  0, 1, 0, 1, 1, 7;
%e A174497    7,  1, 3, 0, 1, 3, 5, 1;
%e A174497   13, 13, 1, 3, 1, 1, 0, 1, 3;
%t A174497 Table[Mod[Prime[n], Prime[n+1]-Prime[k]], {n,12}, {k,n}]//Flatten (* _G. C. Greubel_, Apr 10 2024 *)
%o A174497 (Sage) A174497 = flatten([[nth_prime(n) % (nth_prime(n+1)-nth_prime(k)) for k in range(1,n+1)] for n in range(1, 20)]) # _D. S. McNeil_, Nov 30 2010
%o A174497 (PARI) T(n, k) = prime(n) % (prime(n+1)-prime(k));
%o A174497 tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n, k), ", ")); print); \\ _Michel Marcus_, Aug 08 2017
%o A174497 (Magma)
%o A174497 [NthPrime(n) mod (NthPrime(n+1) - NthPrime(k)): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Apr 10 2024
%Y A174497 Cf. A000040, A086800, A177226.
%K A174497 nonn,tabl,easy
%O A174497 1,7
%A A174497 _Juri-Stepan Gerasimov_, Nov 28 2010