A348357 -id:A348357 - cp's OEIS frontend

A348356 Square array T(n, k), n, k > 0, read by antidiagonal upwards; the k-th column contains, in ascending order, the integers m such that A348330(m) = k.

1, 2, 3, 4, 5, 6, 8, 9, 7, 10, 16, 18, 14, 11, 12, 32, 36, 28, 22, 13, 15, 64, 72, 56, 44, 26, 17, 19, 128, 144, 112, 88, 52, 33, 20, 21, 256, 288, 224, 176, 104, 66, 40, 23, 24, 512, 576, 448, 352, 208, 132, 80, 45, 25, 27, 1024, 1152, 896, 704, 416, 264, 160, 90, 50, 29, 30, 2048, 2304, 1792, 1408, 832, 528, 320, 180, 100, 57, 31, 34

Offset: 1

Rémy Sigrist, Oct 14 2021

When interpreted as a flat array, we have a permutation of the positive integers.

			Array T(n, k) begins:
  n\k|    1     2     3     4     5     6     7     8     9    10
  ---+-----------------------------------------------------------
    1|    1     3     6    10    12    15    19    21    24    27
    2|    2     5     7    11    13    17    20    23    25    29
    3|    4     9    14    22    26    33    40    45    50    57
    4|    8    18    28    44    52    66    80    90   100   114
    5|   16    36    56    88   104   132   160   180   200   228
    6|   32    72   112   176   208   264   320   360   400   456
    7|   64   144   224   352   416   528   640   720   800   912
    8|  128   288   448   704   832  1056  1280  1440  1600  1824
    9|  256   576   896  1408  1664  2112  2560  2880  3200  3648
   10|  512  1152  1792  2816  3328  4224  5120  5760  6400  7296

Rémy Sigrist, PARI program for A348356
Index entries for sequences that are permutations of the natural numbers

Cf. A000079, A348330, A348357.

PARI
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Sum_{i = 1..n-1} T(i, k) < T(n, k).

T(n, 1) = 2^(n-1).

A348330 Lexicographically earliest sequence of positive integers such that for any n > 0, the sum of the indices k < n such that a(k) = a(n) is strictly less than n.

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 3, 1, 2, 4, 4, 5, 5, 3, 6, 1, 6, 2, 7, 7, 8, 4, 8, 9, 9, 5, 10, 3, 10, 11, 11, 1, 6, 12, 12, 2, 13, 13, 14, 7, 14, 15, 15, 4, 8, 16, 16, 17, 17, 9, 18, 5, 18, 19, 19, 3, 10, 20, 20, 21, 21, 11, 22, 1, 22, 6, 23, 23, 24, 12, 24, 2, 25, 25, 26

Offset: 1

Rémy Sigrist, Oct 13 2021

nonn

Every integer appears infinitely many times.

See table A348356 where the integers are arranged according to the present sequence.

Cf. A000079, A348331, A348356, A348357.

s=vector(25); for (n=1, 75, for (k=1, oo, if (s[k]

a(n) = 1 iff n is a power of 2 (A000079).

A348331 Lexicographically earliest sequence of positive integers such that for any n > 0, the sum of the indices k < n such that a(k) = a(n) is less than or equal to n.

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 3, 3, 2, 4, 4, 1, 5, 5, 3, 6, 6, 2, 7, 7, 4, 8, 8, 1, 9, 9, 5, 10, 10, 3, 11, 11, 6, 12, 12, 2, 13, 13, 7, 14, 14, 4, 15, 15, 8, 16, 16, 1, 17, 17, 9, 18, 18, 5, 19, 19, 10, 20, 20, 3, 21, 21, 11, 22, 22, 6, 23, 23, 12, 24, 24, 2, 25, 25, 13

Offset: 1

Rémy Sigrist, Oct 13 2021

nonn

Every integer appears infinitely many times.

See table A348357 where the integers are arranged according to the present sequence.

Cf. A098011, A348330, A348356, A348357.

s=vector(25); for (n=1, 75, for (k=1, oo, if (s[k]<=n, print1 (k", "); s[k]+=n; break)))

a(n) = 1 iff n belongs to A098011.

cp's OEIS Frontend

A348356 Square array T(n, k), n, k > 0, read by antidiagonal upwards; the k-th column contains, in ascending order, the integers m such that A348330(m) = k.

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A348330 Lexicographically earliest sequence of positive integers such that for any n > 0, the sum of the indices k < n such that a(k) = a(n) is strictly less than n.

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A348331 Lexicographically earliest sequence of positive integers such that for any n > 0, the sum of the indices k < n such that a(k) = a(n) is less than or equal to n.

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