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A152722 Triangle read by rows: T(n,0) = prime(n+2), T(n,1) = 1 - T(n,0), T(n,k) = T(n-1,k-1), T(1,0) = 1 T(n,n) = -1.

%I A152722 #28 Jun 01 2025 17:00:34
%S A152722 -1,1,-1,7,-6,-1,11,-10,-6,-1,13,-12,-10,-6,-1,17,-16,-12,-10,-6,-1,
%T A152722 19,-18,-16,-12,-10,-6,-1,23,-22,-18,-16,-12,-10,-6,-1,29,-28,-22,-18,
%U A152722 -16,-12,-10,-6,-1,31,-30,-28,-22,-18,-16,-12,-10,-6,-1,37,-36,-30,-28,-22,-18,-16,-12,-10,-6,-1
%N A152722 Triangle read by rows: T(n,0) = prime(n+2), T(n,1) = 1 - T(n,0), T(n,k) = T(n-1,k-1), T(1,0) = 1 T(n,n) = -1.
%H A152722 G. C. Greubel, <a href="/A152722/b152722.txt">Rows n = 0..50 of triangle, flattened</a>
%F A152722 T(n,n) = -1, T(1,0) = 1, T(n,0) = prime(n+2), T(n,1) = 1 - prime(n+2), T(n,k) = T(n-1,k-1). - _G. C. Greubel_, Apr 07 2019
%e A152722 Triangle begins as:
%e A152722   -1;
%e A152722    1,  -1;
%e A152722    7,  -6,  -1;
%e A152722   11, -10,  -6,  -1;
%e A152722   13, -12, -10,  -6,  -1;
%e A152722   17, -16, -12, -10,  -6,  -1;
%e A152722   19, -18, -16, -12, -10,  -6,  -1;
%e A152722   23, -22, -18, -16, -12, -10,  -6, -1;
%e A152722   29, -28, -22, -18, -16, -12, -10, -6, -1;
%t A152722 T[n_, n_]:= -1; T[1, 0]:= 1; T[n_, 0]:= Prime[n+2]; T[n_, 1]:= 1 - Prime[n+2]; T[n_, k_]:= T[n-1, k-1]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Apr 07 2019 *)
%o A152722 (PARI) {T(n,k) = if(k==n, -1, if(n==1 && k==0, 1, if(k==0, prime(n+2), if(k==1, 1-prime(n+2), T(n-1,k-1) ))))}; \\ _G. C. Greubel_, Apr 07 2019
%o A152722 (Sage)
%o A152722 @CachedFunction
%o A152722 def T(n,k):
%o A152722    if k==n: return -1
%o A152722    elif n==1 and k==0: return 1
%o A152722    elif k==0: return nth_prime(n+2)
%o A152722    elif k==1: return 1 - nth_prime(n+2)
%o A152722    else: return T(n-1,k-1)
%o A152722 [[T(n,k) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Apr 07 2019
%Y A152722 Cf. A152568, A027293.
%K A152722 sign,tabl,less,obsc
%O A152722 0,4
%A A152722 _Roger L. Bagula_ and _Alexander R. Povolotsky_, Dec 11 2008
%E A152722 Edited by _G. C. Greubel_, Apr 07 2019