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A289108 Triangle read by rows: T(n,k) = (k + 1)*prime(n) + k for n > 0, 0 <= k <= n, and with T(0,0) = 1.

%I A289108 #41 Aug 04 2024 20:19:59
%S A289108 1,2,5,3,7,11,5,11,17,23,7,15,23,31,39,11,23,35,47,59,71,13,27,41,55,
%T A289108 69,83,97,17,35,53,71,89,107,125,143,19,39,59,79,99,119,139,159,179,
%U A289108 23,47,71,95,119,143,167,191,215,239,29,59,89,119,149,179,209,239,269,299,329
%N A289108 Triangle read by rows: T(n,k) = (k + 1)*prime(n) + k for n > 0, 0 <= k <= n, and with T(0,0) = 1.
%H A289108 G. C. Greubel, <a href="/A289108/b289108.txt">Rows n = 0..50 of the triangle, flattened</a>
%e A289108 Triangle begins:
%e A289108    1;
%e A289108    2,   5;
%e A289108    3,   7,  11;
%e A289108    5,  11,  17,  23;
%e A289108    7,  15,  23,  31,  39;
%e A289108   11,  23,  35,  47,  59,  71;
%e A289108   13,  27,  41,  55,  69,  83,  97;
%e A289108   17,  35,  53,  71,  89, 107, 125, 143;
%e A289108   19,  39,  59,  79,  99, 119, 139, 159, 179;
%e A289108   23,  47,  71,  95, 119, 143, 167, 191, 215, 239;
%e A289108   ...
%t A289108 Join[{1}, T[n_,k_] := (k + 1) Prime[n] + k; Table[T[n, k], {n, 10}, {k, 0, n}]//Flatten]
%o A289108 (Magma) /* As triangle (here NthPrime(0)=1) */ [[(k+1)*NthPrime(n)+k: k in [0..n]]: n in [0.. 15]];
%o A289108 (SageMath)
%o A289108 def A289108(n,k): return 1 if n==0 else (k+1)*nth_prime(n) +k
%o A289108 flatten([[A289108(n,k) for k in range(n+1)] for n in range(13)]) # _G. C. Greubel_, Aug 04 2024
%Y A289108 Cf. A000040, A008578, A072055.
%K A289108 nonn,tabl
%O A289108 0,2
%A A289108 _Vincenzo Librandi_, Sep 02 2017
%E A289108 Definition corrected by _Bruno Berselli_, Sep 06 2017