A081291 -id:A081291 - cp's OEIS frontend

A082330 Permutation of positive natural numbers: a(n) = A082328(n-1)+1.

1, 2, 4, 3, 5, 9, 10, 8, 6, 7, 12, 13, 11, 14, 23, 24, 27, 26, 28, 22, 25, 20, 15, 16, 21, 18, 17, 19, 32, 33, 35, 36, 37, 31, 34, 29, 30, 39, 40, 41, 38, 42, 65, 66, 69, 68, 70, 78, 79, 77, 74, 75, 82, 83, 81, 84, 64, 67, 76, 73, 80, 62, 71, 57, 43, 44, 58, 46, 45, 47

Offset: 1

Antti Karttunen, Apr 17 2003

nonn

Index entries for sequences that are permutations of the natural numbers

Inverse of A082329. a(n) = A082854(A082326(A081291(n-1))).

A085190 Repeating part of A085191.

Original entry on oeis.org

2, 4, 2, 6, 10, 2, 4, 2, 6, 16, 2, 6, 24, 34, 2, 4, 2, 6, 10, 2, 4, 2, 6, 16, 2, 6, 24, 58, 2, 4, 2, 6, 16, 2, 6, 24, 88, 2, 6, 24, 120, 154, 2, 4, 2, 6, 10, 2, 4, 2, 6, 16, 2, 6, 24, 34, 2, 4, 2, 6, 10, 2, 4, 2, 6, 16, 2, 6, 24, 58, 2, 4, 2, 6, 16, 2, 6, 24, 88, 2, 6, 24, 120, 274, 2, 4, 2, 6, 10

Offset: 0

Antti Karttunen, Jun 14 2003

nonn

Same sequence divided by 2: A085189. Cf. A085193.

a(n) = A085191(A081291(n+1)-1).

A085196 Difference of row 1 and column 1 of the array A085201.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 3, 4, 6, 0, 1, 3, 4, 6, 9, 10, 12, 13, 15, 18, 19, 21, 24, 0, 1, 3, 4, 6, 9, 10, 12, 13, 15, 18, 19, 21, 24, 28, 29, 31, 32, 34, 37, 38, 40, 41, 43, 46, 47, 49, 52, 56, 57, 59, 60, 62, 65, 66, 68, 71, 75, 76, 78, 81, 85, 0, 1, 3, 4, 6, 9, 10, 12, 13, 15, 18, 19, 21

Offset: 0

Antti Karttunen, Jun 14 2003

nonn

The repeating part: A080336 = A085196 o A081291. Cf. A085197.

a(n) = A085223(n) - A072795(n).

A081292 Intersection of A014486 and A079946.

Original entry on oeis.org

0, 12, 50, 52, 56, 202, 204, 210, 212, 216, 226, 228, 232, 240, 810, 812, 818, 820, 824, 842, 844, 850, 852, 856, 866, 868, 872, 880, 906, 908, 914, 916, 920, 930, 932, 936, 944, 962, 964, 968, 976, 992, 3242, 3244, 3250, 3252, 3256, 3274, 3276, 3282, 3284

Offset: 1

Antti Karttunen, Mar 17 2003

nonn

These are A014486-encodings of the binary trees (or equivalent general trees) whose left subtree (equivalently: leftmost branch) is not just a single edge.

Antti Karttunen, Initial terms illustrated in positions 0,3,6,7,8,14,15,16,17,18,...

Cf. A014486, A079946.

a(n) = A014486(A081291(n)).

A082855 a(0)=0, a(1)=1, a(n) = A014137(A081288(n-1)-1).

Original entry on oeis.org

0, 1, 2, 4, 4, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65

Offset: 0

Antti Karttunen, Apr 17 2003

nonn

After n>0, A014137(n) occurs A000245(n) times.

Cf. A081289, A082852. A081291(n) = n+A082855(n+1) for n>0.

A014137(n) = sum(k=0, n, binomial(2*k, k)/(k+1););
A081288(n) = my(i=0); while(binomial(2*i, i)/(i+1) <= n, i++); i;
a(n) = if (n<=1, n, A014137(A081288(n-1)-1)); \\ Michel Marcus, Apr 28 2020

(define (A082855 n) (if (< n 2) n (A014137 (-1+ (A081288 (-1+ n))))))

cp's OEIS Frontend

A082330 Permutation of positive natural numbers: a(n) = A082328(n-1)+1.

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A085190 Repeating part of A085191.

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A085196 Difference of row 1 and column 1 of the array A085201.

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A081292 Intersection of A014486 and A079946.

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A082855 a(0)=0, a(1)=1, a(n) = A014137(A081288(n-1)-1).

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