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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A132673 a(1)=1, a(n) = 9*a(n-1) if the minimal positive integer number not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.

Original entry on oeis.org

1, 9, 8, 7, 6, 5, 4, 3, 2, 18, 17, 16, 15, 14, 13, 12, 11, 10, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37
Offset: 1

Views

Author

Hieronymus Fischer, Sep 15 2007

Keywords

Comments

Also: a(1)=1, a(n) = maximal positive number < a(n-1) not yet in the sequence, if it exists, else a(n) = 9*a(n-1).
Also: a(1)=1, a(n) = a(n-1) - 1, if a(n-1) - 1 > 0 and has not been encountered so far, else a(n) = 9*a(n-1).
A permutation of the positive integers. The sequence is self-inverse, in that a(a(n)) = n.

Crossrefs

For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n) = p*a(n-1) ...) see A132374.
For p=2 to p=10 see A132666 through A132674.

Formula

G.f.: g(x) = (x(1-2x)/(1-x) + 9x^2*f'(x^(17/8)) + (17/81)*(f'(x^(1/8)) - 9x - 1)/(1-x) where f(x) = Sum_{k>=0} x^(9^k) and f'(z) = derivative of f(x) at x = z.
a(n) = (26*9^(r/2) - 10)/8 - n if both r and s are even, else a(n) = (107*9^((s-1)/2) - 10)/8 - n, where r = ceiling(2*log_9((8n+9)/17)) and s = ceiling(2*log_9(8n+9)/8)) - 1.
a(n) = (9^floor(1 + (k+1)/2) + 17*9^floor(k/2) - 10)/8 - n, where k=r if r is odd, else k=s (with respect to r and s above; formally, k = ((r+s) - (r-s)*(-1)^r)/2).

A132670 a(1)=1, a(n) = 6*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.

Original entry on oeis.org

1, 6, 5, 4, 3, 2, 12, 11, 10, 9, 8, 7, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49
Offset: 1

Views

Author

Hieronymus Fischer, Sep 15 2007

Keywords

Comments

Also: a(1)=1, a(n) = maximal positive integer < a(n-1) not yet in the sequence, if it exists, else a(n) = 6*a(n-1).
Also: a(1)=1, a(n) = a(n-1) - 1, if a(n-1) - 1 > 0 and has not been encountered so far, else a(n) = 6*a(n-1).
A permutation of the positive integers. The sequence is self-inverse, in that a(a(n)) = n.

Crossrefs

For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n)=p*a(n-1) ...) see A132374.
For p=2 to p=10 see A132666 through A132674.

Formula

G.f.: g(x) = (x(1-2x)/(1-x) + 6x^2*f'(x^(11/5)) + (11/36)*(f'(x^(1/5)) - 6x - 1)/(1-x) where f(x) = Sum_{k>=0} x^(6^k) and f'(z) = derivative of f(x) at x = z.
a(n) = (17*6^(r/2) - 7)/5 - n if both r and s are even, else a(n) = (47*6^((s-1)/2) - 7)/5 - n, where r = ceiling(2*log_6((5n+6)/11)) and s = ceiling(2*log_6((5n+6)/6)) - 1.
a(n) = (6^floor(1 + (k+1)/2) + 11*6^floor(k/2) - 7)/5 - n, where k=r if r is odd, else k=s (with respect to r and s above; formally, k = ((r+s) - (r-s)*(-1)^r)/2).

A132671 a(1)=1, a(n) = 7*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.

Original entry on oeis.org

1, 7, 6, 5, 4, 3, 2, 14, 13, 12, 11, 10, 9, 8, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92
Offset: 1

Views

Author

Hieronymus Fischer, Sep 15 2007

Keywords

Comments

Also: a(1)=1, a(n) = maximal positive integer < a(n-1) not yet in the sequence, if it exists, else a(n) = 7*a(n-1).
Also: a(1)=1, a(n) = a(n-1) - 1, if a(n-1) - 1 > 0 and has not been encountered so far, else a(n) = 7*a(n-1).
A permutation of the positive integers. The sequence is self-inverse, in that a(a(n)) = n.

Crossrefs

For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n) = p*a(n-1) ...) see A132374.
For p=2 to p=10 see A132666 through A132674.

Formula

G.f.: g(x) = (x(1-2x)/(1-x) + 7x^2*f'(x^(13/6)) + (13/49)*(f'(x^(1/6)) - 7x - 1)/(1-x) where f(x) = Sum_{k>=0} x^(7^k) and f'(z) = derivative of f(x) at x = z.
a(n) = (20*7^(r/2) - 8)/6 - n if both r and s are even, else a(n) = (62*7^((s-1)/2) - 8)/6 - n, where r = ceiling(2*log_7((6n+7)/13)) and s = ceiling(2*log_7(6n+7)/6)) - 1.
a(n) = (7^floor(1 + (k+1)/2) + 13*7^floor(k/2) - 8)/6 - n, where k=r if r is odd, else k=s (with respect to r and s above; formally, k = ((r+s) - (r-s)*(-1)^r)/2).

A132672 a(1)=1, a(n) = 8*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.

Original entry on oeis.org

1, 8, 7, 6, 5, 4, 3, 2, 16, 15, 14, 13, 12, 11, 10, 9, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17
Offset: 1

Views

Author

Hieronymus Fischer, Sep 15 2007

Keywords

Comments

Also: a(1)=1, a(n) = maximal positive integer < a(n-1) not yet in the sequence, if it exists, else a(n) = 8*a(n-1).
Also: a(1)=1, a(n) = a(n-1) - 1, if a(n-1) - 1 > 0 and has not been encountered so far, else a(n) = 8*a(n-1).
A permutation of the positive integers. The sequence is self-inverse, in that a(a(n)) = n.

Crossrefs

For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n)=p*a(n-1) ...) see A132374.
For p=2 to p=10 see A132666 through A132674.

Formula

G.f.: g(x) = (x(1-2x)/(1-x) + 8x^2*f'(x^(15/7)) + (15/64)*(f'(x^(1/7)) - 8x-1)/(1-x) where f(x) = Sum_{k>=0} x^(8^k) and f'(z) = derivative of f(x) at x = z.
a(n) = (23*8^(r/2) - 9)/7 - n if both r and s are even, else a(n) = (78*8^((s-1)/2) - 9)/7 - n, where r = ceiling(2*log_8((7n+8)/15)) and s = ceiling(2*log_8(7n+8)/7)) - 1.
a(n) = (8^floor(1 + (k+1)/2) + 15*8^floor(k/2) - 9)/7 - n, where k=r if r is odd, else k=s (with respect to r and s above; formally, k = ((r+s) - (r-s)*(-1)^r)/2).
Previous Showing 11-14 of 14 results.

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