A335910 Square array where row n lists all numbers k for which A335885(k) = n, read by falling antidiagonals.

1, 2, 3, 4, 5, 9, 8, 6, 11, 27, 16, 7, 13, 33, 81, 32, 10, 15, 37, 99, 243, 64, 12, 18, 39, 107, 297, 729, 128, 14, 19, 43, 109, 321, 891, 2187, 256, 17, 21, 45, 111, 327, 963, 2673, 6561, 512, 20, 22, 53, 117, 333, 981, 2889, 8019, 19683, 1024, 24, 23, 54, 121, 351, 999, 2943, 8667, 24057, 59049, 2048, 28, 25, 55, 129, 363, 1053, 2997, 8829, 26001, 72171, 177147

Offset

0,2

Comments

Array is read by descending antidiagonals with (n,k) = (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), ... where A(n,k) is the (k+1)-th solution x to A335885(x) = n. The row indexing (n) starts from 0, and column indexing (k) also from 0.

For any odd prime p that appears on row n, either p-1 or p+1 appears on row n-1.

The e-th powers of the terms on row n form a subset of terms on row (e*n). More generally, a product of terms that occur on rows i_1, i_2, ..., i_k can be found at row (i_1 + i_2 + ... + i_k), because A335885 is completely additive.

Links

Table of n, a(n) for n=0..77.

Index entries for sequences that are permutations of the natural numbers

Example

The top left corner of the array:
n\k |     0      1      2      3      4      5      6      7      8      9
----+--------------------------------------------------------------------------
  0 |     1,     2,     4,     8,    16,    32,    64,   128,   256,   512, ...
  1 |     3,     5,     6,     7,    10,    12,    14,    17,    20,    24, ...
  2 |     9,    11,    13,    15,    18,    19,    21,    22,    23,    25, ...
  3 |    27,    33,    37,    39,    43,    45,    53,    54,    55,    57, ...
  4 |    81,    99,   107,   109,   111,   117,   121,   129,   131,   135, ...
  5 |   243,   297,   321,   327,   333,   351,   363,   387,   393,   405, ...
  6 |   729,   891,   963,   981,   999,  1053,  1089,  1161,  1177,  1179, ...
  7 |  2187,  2673,  2889,  2943,  2997,  3159,  3267,  3483,  3531,  3537, ...
  8 |  6561,  8019,  8667,  8829,  8991,  9477,  9801, 10449, 10593, 10611, ...
  9 | 19683, 24057, 26001, 26487, 26973, 28431, 29403, 31347, 31779, 31833, ...

Prog

(PARI)
up_to = 78-1; \\ = binomial(12+1, 2)-1.
memoA335885 = Map();
A335885(n) = if(1==n, 0, my(v=0); if(mapisdefined(memoA335885, n, &v), v, my(f=factor(n)); v = sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(1+min(A335885(f[k, 1]-1), A335885(f[k, 1]+1))))); mapput(memoA335885, n, v); (v)));
memoA335910sq = Map();
A335910sq(n, k) = { my(v=0); if((0==k), v = -1, if(!mapisdefined(memoA335910sq, [n, k-1], &v), v = A335910sq(n, k-1))); for(i=1+v, oo, if(A335885(1+i)==n, mapput(memoA335910sq, [n, k], i); return(1+i))); };
A335910list(up_to) = { my(v = vector(1+up_to), i=0); for(a=0, oo, for(col=0, a, i++; if(i > #v, return(v)); v[i] = A335910sq(col, (a-(col))))); (v); };
v335910 = A335910list(up_to);
A335910(n) = v335910[1+n];
for(n=0, up_to, print1(A335910(n), ", "));

Crossrefs

Cf. A335885.

Cf. A000079, A335911, A335912 (rows 0-2), A000244 (is very like the leftmost column).

Cf. also arrays A334100, A335430.

Sequence in context: A164340 A046021 A319023 * A362814 A371152 A266531

Adjacent sequences: A335907 A335908 A335909 * A335911 A335912 A335913

Keyword

nonn,tabl

Author

Antti Karttunen, Jul 01 2020

Status

approved