A082011 Square array read by antidiagonals, alternating upwards and downwards: T(1,1) = 2 and every other entry is the smallest prime not already used such that the n-th antidiagonal sum is a multiple of n.

2, 3, 5, 7, 13, 19, 11, 17, 23, 29, 31, 37, 41, 43, 53, 47, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 113, 107, 109, 127, 131, 137, 139, 149, 157, 151, 163, 167, 173, 179, 181, 191, 197, 227, 193, 199, 211, 223, 229, 233, 239, 241, 251, 271, 257, 263, 269, 277

Offset

1,1

Comments

This is the boustrophedon method of filling an array.

Links

Alois P. Heinz, Antidiagonals n = 1..45, flattened

Example

Square array begins:
2,   3,  19,  11,  53,  47, ...
5,  13,  17,  43,  59, 103, ...
7,  23,  41,  61, 101, 127, ...
29, 37,  67,  97, 131, 181, ...
31, 71,  89, 137, 179, 229, ...
73, 83, 139, 173, 233, 283, ...
T(2,2) = 13 and not 11, because otherwise T(1,3)+7+11 = 0 (mod 3) would not be satisfied for any prime.

Maple

b:= proc(t) false end: T:= proc(n, k) local h, t, l, m; if n<1 or k<1 then t:=0 else h:= 1- 2* irem(n+k, 2); m:= n+k-1; l:= add(T(n+h*t, k-h*t), t=1..m-1); t:=3; while b(t) or (h=1 and (n=2 and igcd(t+l, m)>1 or n=1 and irem(t+l, m)<>0)) or (h=-1 and (k=2 and igcd(t+l, m)>1 or k=1 and irem(t+l, m)<>0)) do t:= nextprime(t) od fi; b(t):= true; T(n, k):=t end: T(1, 1):=2: seq(`if`(irem(d, 2)=1, seq(T(1+d-k, k), k=1..d), seq(T(n, 1+d-n), n=1..d)), d=1..15);  # Alois P. Heinz, Oct 10 2009

Mathematica

Clear[b]; b[_] = False; T[n_, k_] := Module[{h, t, l, m}, If[n<1 || k<1, t = 0, h = 1 - 2*Mod[n+k, 2]; m = n+k-1; l = Sum[T[n + h*t, k - h*t], {t, 1, m-1}]; t = 3; While[b[t] || (h == 1 && (n == 2 && GCD[t+l, m]>1 || n == 1 && Mod[t+l, m] != 0)) || (h == -1 && (k == 2 && GCD[t+l, m]>1 || k == 1 && Mod[t+l, m] != 0)), t = NextPrime[t]]]; b[t] = True; T[n, k] = t]; T[1, 1] = 2; Table[If[Mod[d, 2] == 1, Table[T[1+d-k, k], {k, 1, d}], Table [T[n, 1+d-n], {n, 1, d}]], {d, 1, 15}] // Flatten (* Jean-François Alcover, Jun 10 2015, after Alois P. Heinz *)

Crossrefs

Cf. A082012, A082013, A082014, A082015.

Sequence in context: A362778 A362779 A077316 * A101044 A077321 A216437

Adjacent sequences: A082008 A082009 A082010 * A082012 A082013 A082014

Keyword

nonn,tabl

Author

Amarnath Murthy, Apr 05 2003

Extensions

Edited with more terms by Alois P. Heinz, Oct 10 2009

Status

approved