A287919 Square array T(0,n) = prime(n) and T(m+1,n) = T(m,n) + T(m,n+1), m >= 0, n >= 1, read by falling antidiagonals.

2, 3, 5, 5, 8, 13, 7, 12, 20, 33, 11, 18, 30, 50, 83, 13, 24, 42, 72, 122, 205, 17, 30, 54, 96, 168, 290, 495, 19, 36, 66, 120, 216, 384, 674, 1169, 23, 42, 78, 144, 264, 480, 864, 1538, 2707, 29, 52, 94, 172, 316, 580, 1060, 1924, 3462, 6169

Offset: 0

Author

M. F. Hasler, Jun 02 2017

Keywords

• nonn
• easy
• tabl

Examples

			The array starts:
[0]    2    3    5     7    11    13    17    19    23    29 ... (A000040)
[1]    5    8   12    18    24    30    36    42    52    60 ... (A001043)
[2]   13   20   30    42    54    66    78    94   112   128 ... (A096277)
[3]   33   50   72    96   120   144   172   206   240   274 ... (A096278)
[4]   83  122  168   216   264   316   378   446   514   582 ... (A096279)
[5]  205  290  384   480   580   694   824   960  1096  1226 ...
[6]  495  674  864  1060  1274  1518  1784  2056  2322  2570 ...
[7] 1169 1538 1924  2334  2792  3302  3840  4378  4892  5380 ...
...
First column is A007443: binomial transform of primes.
Second column is A178167: binomial transform of odd primes.
		

Links

• Seiichi Manyama, Antidiagonals n = 0..139, flattened

Crossrefs

Rows and columns include A001043, A096277-A096279, A007443, A178167.

Programs

Mathematica

A287919list[dmax_]:=With[{a=Reverse[NestList[ListConvolve[{1,1},#]&,Prime[Range[dmax]],dmax-1]]},Array[Reverse[Diagonal[a,#]]&,dmax,1-dmax]];
A287919list[10] (* Generates 10 antidiagonals *) (* Paolo Xausa, Oct 31 2023 *)

PARI

A287919(m,n)=sum(k=0,m,prime(n+k)*binomial(m,k))
/* read by antidiagonals */ for(m=0,13,for(n=0,m,print1(A287919(n,m-n+1)",")))