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A211890 Triangle read by rows, where row n starts with n-th prime, followed by n primes in arithmetic progression; T(0,0) = 1 by convention.

%I A211890 #23 Feb 16 2025 08:33:17
%S A211890 1,2,3,3,5,7,5,11,17,23,7,37,67,97,127,11,71,131,191,251,311,13,
%T A211890 244243,488473,732703,976933,1221163,1465393,17,6947,13877,20807,
%U A211890 27737,34667,41597,48527,19,546859,1093699,1640539,2187379,2734219,3281059,3827899
%N A211890 Triangle read by rows, where row n starts with n-th prime, followed by n primes in arithmetic progression; T(0,0) = 1 by convention.
%C A211890 T(n,0) = A000040(n) and T(n,k+1) - T(n,k) = A211889(n), 0 <= k < n.
%H A211890 Chai Wah Wu, <a href="/A211890/b211890.txt">Rows n=0..10 of triangle, flattened (rows n = 0..9 from Reinhard Zumkeller)</a>
%H A211890 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeArithmeticProgression.html">Prime Arithmetic Progression</a>.
%H A211890 Wikipedia, <a href="http://en.wikipedia.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.
%H A211890 <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>
%e A211890 First 9 rows of triangle:
%e A211890 0:  1
%e A211890 1:  2 3
%e A211890 2:  3 5 7
%e A211890 3:  5 11 17 23
%e A211890 4:  7 37 67 97 127
%e A211890 5:  11 71 131 191 251 311
%e A211890 6:  13 244243 488473 732703 976933 1221163 1465393
%e A211890 7:  17 6947 13877 20807 27737 34667 41597 48527
%e A211890 8:  19 546859 1093699 1640539 2187379 2734219 3281059 3827899 4374739
%o A211890 (Haskell)
%o A211890 a211890 n k = a211890_tabl !! n !! k
%o A211890 a211890_row n = a211890_tabl !! n
%o A211890 a211890_tabl = zipWith3 (\p k row -> map ((+ p) . (* k)) row)
%o A211890                         a008578_list (0 : a211889_list) a002262_tabl
%Y A211890 Cf. A007528, A007652, A132231, A214360, A008578, A002262.
%K A211890 nonn,tabl
%O A211890 0,2
%A A211890 _Reinhard Zumkeller_, Jul 13 2012