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

Offset: 0

Author

Roger L. Bagula and Alexander R. Povolotsky, Dec 11 2008

Keywords

• sign
• tabl
• less
• obsc

Examples

			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;
		

Links

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

Crossrefs

Cf. A152568, A027293.

Programs

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 *)

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

Sage

@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

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

Extensions

Edited by G. C. Greubel, Apr 07 2019