A354930 Square array where the row n lists all nonnegative numbers k for which A345992(k) = n, read by falling antidiagonals.

1, 2, 6, 3, 10, 12, 4, 14, 21, 20, 5, 18, 39, 36, 15, 7, 22, 48, 52, 30, 42, 8, 26, 57, 68, 40, 78, 28, 9, 34, 75, 84, 55, 114, 35, 24, 11, 38, 93, 100, 65, 150, 56, 72, 45, 13, 46, 111, 116, 80, 186, 77, 88, 63, 110, 16, 50, 129, 148, 115, 222, 105, 136, 90, 310, 33, 17, 54, 147, 164, 130, 258, 133, 152, 126, 410, 44, 156

Offset: 1

Author

Antti Karttunen, Jun 14 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), ... where A(n,k) is the k-th solution x to A345992(x) = n.

Examples

			The top left 15x9 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 |  6, 10,  14,  18,  22,  26,  34,  38,  46,  50,  54,  58,  62,  74,  82,
  3 | 12, 21,  39,  48,  57,  75,  93, 111, 129, 147, 183, 192, 201, 219, 237,
  4 | 20, 36,  52,  68,  84, 100, 116, 148, 164, 196, 212, 228, 244, 292, 324,
  5 | 15, 30,  40,  55,  65,  80, 115, 130, 155, 180, 205, 215, 230, 255, 265,
  6 | 42, 78, 114, 150, 186, 222, 258, 294, 366, 402, 438, 474, 582, 618, 654,
  7 | 28, 35,  56,  77, 105, 133, 154, 175, 203, 224, 273, 301, 329, 350, 371,
  8 | 24, 72,  88, 136, 152, 200, 216, 264, 328, 344, 392, 456, 472, 536, 584,
  9 | 45, 63,  90, 126, 144, 171, 207, 225, 252, 288, 333, 369, 387, 414, 450,
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A344005, A345992.

Column 1: A354931.

Rows 1..3: A000961, A278568 (without its initial 2, conjectured), A354984 (conjectured).

See also array A354940 where the entries are divided by their row index.

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))); };
A354930list(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] = A354930sq(col,(a-(col-1))))); (v); };
v354930 = A354930list(up_to);
A354930(n) = v354930[n];