A354940 Square array A(n, k) = A354930(n, k)/n, read by falling antidiagonals.

1, 2, 3, 3, 5, 4, 4, 7, 7, 5, 5, 9, 13, 9, 3, 7, 11, 16, 13, 6, 7, 8, 13, 19, 17, 8, 13, 4, 9, 17, 25, 21, 11, 19, 5, 3, 11, 19, 31, 25, 13, 25, 8, 9, 5, 13, 23, 37, 29, 16, 31, 11, 11, 7, 11, 16, 25, 43, 37, 23, 37, 15, 17, 10, 31, 3, 17, 27, 49, 41, 26, 43, 19, 19, 14, 41, 4, 13, 19, 29, 61, 49, 31, 49, 22, 25, 16, 51, 6, 25, 7

Offset: 1

Author

Antti Karttunen, Jun 15 2022

Keywords

• nonn
• tabl

Comments

Array is read by descending antidiagonals with (n,k) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), etc.

Examples

			The top left 15x16 corner of the array:
n\k  |  1   2   3   4   5   6   7   8    9   10   11   12   13   14   15
-----+---------------------------------------------------------------------
   1 |  1,  2,  3,  4,  5,  7,  8,  9,  11,  13,  16,  17,  19,  23,  25,
   2 |  3,  5,  7,  9, 11, 13, 17, 19,  23,  25,  27,  29,  31,  37,  41,
   3 |  4,  7, 13, 16, 19, 25, 31, 37,  43,  49,  61,  64,  67,  73,  79,
   4 |  5,  9, 13, 17, 21, 25, 29, 37,  41,  49,  53,  57,  61,  73,  81,
   5 |  3,  6,  8, 11, 13, 16, 23, 26,  31,  36,  41,  43,  46,  51,  53,
   6 |  7, 13, 19, 25, 31, 37, 43, 49,  61,  67,  73,  79,  97, 103, 109,
   7 |  4,  5,  8, 11, 15, 19, 22, 25,  29,  32,  39,  43,  47,  50,  53,
   8 |  3,  9, 11, 17, 19, 25, 27, 33,  41,  43,  49,  57,  59,  67,  73,
   9 |  5,  7, 10, 14, 16, 19, 23, 25,  28,  32,  37,  41,  43,  46,  50,
  10 | 11, 31, 41, 51, 61, 71, 81, 91, 101, 121, 131, 141, 151, 171, 181,
  11 |  3,  4,  6,  9, 12, 15, 17, 23,  25,  28,  31,  34,  37,  45,  47,
  12 | 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 145, 157, 169, 181, 193,
  13 |  7,  8,  9, 11, 14, 20, 22, 23,  27,  33,  37,  40,  46,  47,  48,
  14 |  5, 15, 19, 29, 43, 47, 57, 61,  71,  89,  99, 103, 113, 127, 131,
  15 |  4,  8, 16, 19, 23, 31, 38, 46,  49,  53,  61,  64,  76,  79,  83,
  16 |  7, 11, 13, 17, 23, 27, 29, 33,  43,  49,  59,  61,  65,  71,  75,
		

Crossrefs

Cf. A345992, A354930.

Cf. A354932 (column 1).

Rows 1 .. 7 (some of these are conjectural): A000961, A061345 (without its initial 1), A137827, A354934, A354935, A354936, A354937, A354938, A354939.

Programs

PARI

up_to = 105;
A345992(n) = for(m=1, oo, if((m*(m+1))%n==0, return(gcd(n,m))));
memoA354930sq = Map();
A354930sq(n, k) = { my(v=0); if(!mapisdefined(memoA354930sq,[n,k-1],&v),if(1==k, v=0, v = A354930sq(n, k-1))); for(i=1+v,oo,if(A345992(i)==n,mapput(memoA354930sq,[n,k],i); return(i))); };
A354940sq(n, k) = (A354930sq(n, k)/n);
A354940list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A354940sq(col,(a-(col-1))))); (v); };
v354940 = A354940list(up_to);
A354940(n) = v354940[n];