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%I #16 Sep 09 2017 03:56:16
%S 1,0,1,0,1,2,1,2,2,2,3,4,1,3,1,2,3,4,1,4,0,2,4,3,4,2,2,1,4,6,2,5,2,3,
%T 1,2,5,6,3,4,2,4,2,2,2,6,7,2,6,1,5,1,3,2,6,5,7,4,2,4,5,4,3,2,2,4,7,7,
%U 3,7,2,3,3,4,3,7,2,3,11,3,5,3,9,2,4,1,5,3,9,2,4,8,5,9,4,6,2,4,2,8,4,6,2,4,2
%N Triangle where a(0,0) = 1; a(n,m) = number of terms in row (n-1) which, when added to m, are primes.
%H Michael De Vlieger, <a href="/A114920/b114920.txt">Table of n, a(n) for n = 0..11627</a> (rows 0 <= n <= 150).
%e Row 3 of the triangle is [1,2,2,2]. Adding 0 to these gives [1,2,2,2], of which 3 terms are primes. Adding 1 to these gives [2,3,3,3], of which 4 terms are primes. Adding 2 to these gives [3,4,4,4], of which one term is prime. Adding 3 to these gives [4,5,5,5], of which 3 terms are primes. Adding 4 to these gives [5,6,6,6], of which one term is prime. So row 4 is [3,4,1,3,1].
%e Triangle begins:
%e 1;
%e 0, 1;
%e 0, 1, 2;
%e 1, 2, 2, 2;
%e 3, 4, 1, 3, 1;
%e 2, 3, 4, 1, 4, 0;
%e 2, 4, 3, 4, 2, 2, 1;
%e ...
%t NestList[Function[w, Map[Function[k, Count[Map[k + # &, w], _?PrimeQ]], Range[0, Length@ w]]], {1}, 13] // Flatten (* _Michael De Vlieger_, Sep 07 2017 *)
%o (PARI) {v=[1]; for(k=1,20,w=vector(length(v)+1);for(i=0,length(v), for(j=1,length(v),if(isprime(v[j]+i),w[i+1]++)));v=w;print(v))} \\ Lambert Herrgesell(zero815(AT)googlemail.com), Jan 13 2006
%Y Cf. A114919, A114905, A114906.
%K nonn,tabl
%O 0,6
%A _Leroy Quet_, Jan 07 2006
%E More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Jan 13 2006
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