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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.

-1, 1, -1, 7, -6, -1, 11, -10, -6, -1, 13, -12, -10, -6, -1, 17, -16, -12, -10, -6, -1, 19, -18, -16, -12, -10, -6, -1, 23, -22, -18, -16, -12, -10, -6, -1, 29, -28, -22, -18, -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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

G. C. Greubel, Rows n = 0..50 of triangle, flattened

FORMULA

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

EXAMPLE

Triangle begins as:

-1;

1, -1;

7, -6, -1;

11, -10, -6, -1;

13, -12, -10, -6, -1;

17, -16, -12, -10, -6, -1;

19, -18, -16, -12, -10, -6, -1;

23, -22, -18, -16, -12, -10, -6, -1;

29, -28, -22, -18, -16, -12, -10, -6, -1;

MATHEMATICA

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 *)

PROG

(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

(SageMath)

@CachedFunction

def T(n, k):

if k==n: return -1

elif n==1 and k==0: return 1

elif k==0: return nth_prime(n+2)

elif k==1: return 1 - nth_prime(n+2)

else: return T(n-1, k-1)

[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Apr 07 2019

CROSSREFS