A348356 -id:A348356 - cp's OEIS frontend

A348357 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 A348331(m) = k.

1, 2, 4, 3, 5, 7, 6, 9, 8, 10, 12, 18, 15, 11, 13, 24, 36, 30, 21, 14, 16, 48, 72, 60, 42, 27, 17, 19, 96, 144, 120, 84, 54, 33, 20, 22, 192, 288, 240, 168, 108, 66, 39, 23, 25, 384, 576, 480, 336, 216, 132, 78, 45, 26, 28, 768, 1152, 960, 672, 432, 264, 156, 90, 51, 29, 31

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     4     7    10    13    16    19    22    25    28
    2|    2     5     8    11    14    17    20    23    26    29
    3|    3     9    15    21    27    33    39    45    51    57
    4|    6    18    30    42    54    66    78    90   102   114
    5|   12    36    60    84   108   132   156   180   204   228
    6|   24    72   120   168   216   264   312   360   408   456
    7|   48   144   240   336   432   528   624   720   816   912
    8|   96   288   480   672   864  1056  1248  1440  1632  1824
    9|  192   576   960  1344  1728  2112  2496  2880  3264  3648
   10|  384  1152  1920  2688  3456  4224  4992  5760  6528  7296

Rémy Sigrist, PARI program for A348357
Index entries for sequences that are permutations of the natural numbers

Cf. A098011, A348331, A348356.

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

T(n, 1) = A098011(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

A348357 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 A348331(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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