A096369 Triangle read by rows, 0<=k

0, 1, 2, 2, 1, 2, 2, 1, 1, 2, 5, 3, 3, 2, 5, 7, 3, 4, 5, 3, 7, 13, 7, 6, 6, 4, 7, 13, 23, 13, 12, 9, 10, 12, 11, 23, 43, 22, 23, 22, 23, 22, 21, 21, 43, 75, 37, 37, 36, 40, 39, 38, 38, 37, 75, 137, 71, 71, 73, 66, 56, 71, 70, 66, 67, 137, 255, 128, 125, 130, 127, 132, 128, 130, 129, 126, 125, 255

Offset: 1

Author

Reinhard Zumkeller, Jul 19 2004

Keywords

• nonn
• tabl

Comments

T(n,0) = A036378(n-1) for n>1; T(n,n-1) = T(n,0) for n>2;

T(n,1) = A095008(n-1) for n>2;

T(n,n-2) = A095766(n-1) for n>1;

conjecture: T(n,k) > 0 for n>1.

Examples

			prime(12) = 37 -> 1 0 0 1 0 1 ..... n = 6
prime(13) = 41 -> 1 0 1 0 0 1 ..... all primes p:
prime(14) = 43 -> 1 0 1 0 1 1 ..... 2^(6-1) <= p < 2^6
prime(15) = 47 -> 1 0 1 1 1 1
prime(16) = 53 -> 1 1 0 1 0 1
prime(17) = 59 -> 1 1 1 0 1 1
prime(18) = 61 -> 1 1 1 1 0 1
col-sums of bits: 7 3 5 4 3 7 : T(6,5)=7, T(6,4)=3, T(6,3)=5,
...
		

Programs

Mathematica

S[n_] := S[n] = IntegerDigits[Select[Range[2^(n-1), 2^n], PrimeQ], 2] // Transpose;
T[1, 1] = 0;
T[n_, k_] := S[n][[n-k+1]] // Total;
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 14 2021 *)