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%I #20 Jul 21 2023 04:27:24
%S 2,3,5,5,7,11,7,9,13,11,13,17,23,13,15,19,25,17,19,23,29,37,19,21,25,
%T 31,39,23,25,29,35,43,29,31,35,41,49,31,33,37,43,51,61,37,39,43,49,57,
%U 67,41,43,47,53,61,71,83,43,45,49,55,63,73,85,47,49,53,59,67,77,89
%N Irregular triangle T(n, k) = prime(n) + k*(k-1), for n >= 1 and 1 <= k <= 1 + A000720(n), read by rows.
%H G. C. Greubel, <a href="/A120724/b120724.txt">Rows n = 1..100 of the irregular triangle, flattened</a>
%F T(n, k) = prime(k) + 2*Sum_{j=1..n-1} j, for n >= 1 and 1 <= k <= 1 + A000720(n).
%F T(n, k) = prime(n) + k*(k-1).
%e Irregular triangle begins as:
%e 2;
%e 3, 5;
%e 5, 7, 11;
%e 7, 9, 13;
%e 11, 13, 17, 23;
%e 13, 15, 19, 25;
%e 17, 19, 23, 29, 37;
%e 19, 21, 25, 31, 39;
%e 23, 25, 29, 35, 43;
%e 29, 31, 35, 41, 49;
%t T[n_, k_]:= Prime[n] + k*(k-1);
%t Table[T[n,k], {n,20}, {k,PrimePi[n]+1}]//Flatten
%o (Magma)
%o A120724:= func< n,k | NthPrime(n) +k*(k-1) >;
%o [A120724(n,k): k in [1..#PrimesUpTo(n)+1], n in [1..20]]; // _G. C. Greubel_, Jul 20 2023
%o (SageMath)
%o def A120724(n,k): return nth_prime(n) + k*(k-1)
%o flatten([[A120724(n,k) for k in range(1,prime_pi(n)+2)] for n in range(1,21)]) # _G. C. Greubel_, Jul 20 2023
%Y Cf. A000040, A000720.
%K nonn,tabf,easy
%O 1,1
%A _Roger L. Bagula_, Aug 18 2006
%E Edited by _G. C. Greubel_, Jul 20 2023
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