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