A220516 Nonnegative integers in square maze arrangement T(n,k), read by antidiagonals, n>=0, k>=0.

0, 1, 3, 8, 2, 4, 9, 7, 5, 15, 24, 10, 6, 14, 16, 25, 23, 11, 13, 17, 35, 48, 26, 22, 12, 18, 34, 36, 49, 47, 27, 21, 19, 33, 37, 63, 80, 50, 46, 28, 20, 32, 38, 62, 64, 81, 79, 51, 45, 29, 31, 39, 61, 65, 99, 120, 82, 78, 52, 44, 30, 40, 60, 66, 98, 100

Offset

0,3

Comments

This sequence consists of 0 together with a permutation of the natural numbers. The structure is the same as A081344 but starting with 0, not 1.

It appears that in the n-th layer there is at least a prime number <= g and also there is at least a prime number > g, where g is the number on the main diagonal, the n-th oblong number A002378(n), if n >= 1.

Links

Table of n, a(n) for n=0..65.

Index entries for sequences that are permutations of the nonnegative integers

Formula

a(n) = A081344(n+1) - 1.

T(n,k) = n^2 + k , if n is odd and k<=n.

T(n,k) = n(n + 2) - k, if n is even and k<=n.

T(n,k) = k(k + 2) - n, if n is odd and n<k.

T(n,k) = k^2 + n , if n is even and n<k.

Example

The first layer is [1, 2, 3] which looks like this:
.  3,
1, 2,
The second layer is [4, 5, 6, 7, 8] which looks like this:
.  .  4
.  .  5,
8, 7, 6,
Square array T(0,0)..T(10,10) begins:
0,     3,   4,  15,  16,  35,  36,  63,  64,  99, 100,...
1,     2,   5,  14,  17,  34,  37,  62,  65,  98, 101,...
8,     7,   6,  13,  18,  33,  38,  61,  66,  97, 102,...
9,    10,  11,  12,  19,  32,  39,  60,  67,  96, 103,...
24,   23,  22,  21,  20,  31,  40,  59,  68,  95, 104,...
25,   26,  27,  28,  29,  30,  41,  58,  69,  94, 105,...
48,   47,  46,  45,  44,  43,  42,  57,  70,  93, 106,...
49,   50,  51,  52,  53,  54,  55,  56,  71,  92, 107,...
80,   79,  78,  77,  76,  75,  74,  73,  72,  91, 108,...
81,   82,  83,  84,  85,  86,  87,  88,  89,  90, 109,...
120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110,...
...

Crossrefs

Main diagonal is A002378.

Cf. A000040, A000290, A002620, A081344, A220508.

Sequence in context: A195426 A202537 A356418 * A010627 A103712 A374971

Adjacent sequences: A220513 A220514 A220515 * A220517 A220518 A220519

Keyword

nonn,tabl

Author

Omar E. Pol, Feb 09 2013

Status

approved