A082011 - OEIS

%I #15 Jun 10 2015 10:01:11

%S 2,3,5,7,13,19,11,17,23,29,31,37,41,43,53,47,59,61,67,71,73,79,83,89,

%T 97,101,103,113,107,109,127,131,137,139,149,157,151,163,167,173,179,

%U 181,191,197,227,193,199,211,223,229,233,239,241,251,271,257,263,269,277

%N 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.

%C This is the boustrophedon method of filling an array.

%H Alois P. Heinz, <a href="/A082011/b082011.txt">Antidiagonals n = 1..45, flattened</a>

%e Square array begins:

%e 2,   3,  19,  11,  53,  47, ...

%e 5,  13,  17,  43,  59, 103, ...

%e 7,  23,  41,  61, 101, 127, ...

%e 29, 37,  67,  97, 131, 181, ...

%e 31, 71,  89, 137, 179, 229, ...

%e 73, 83, 139, 173, 233, 283, ...

%e T(2,2) = 13 and not 11, because otherwise T(1,3)+7+11 = 0 (mod 3) would not be satisfied for any prime.

%p 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

%t 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_ *)

%Y Cf. A082012, A082013, A082014, A082015.

%K nonn,tabl

%O 1,1

%A _Amarnath Murthy_, Apr 05 2003

%E Edited with more terms by _Alois P. Heinz_, Oct 10 2009