cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A278504 Inverse permutation to A278503.

Original entry on oeis.org

1, 3, 2, 6, 5, 10, 4, 15, 8, 21, 9, 28, 7, 36, 12, 45, 14, 55, 11, 66, 13, 78, 20, 91, 17, 105, 16, 120, 27, 136, 23, 153, 19, 171, 35, 190, 18, 210, 22, 231, 44, 253, 30, 276, 26, 300, 54, 325, 29, 351, 24, 378, 65, 406, 25, 435, 34, 465, 77, 496, 38, 528, 37, 561, 90, 595, 47, 630, 43, 666, 104, 703, 31, 741, 33, 780, 119, 820, 46
Offset: 1

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Author

Antti Karttunen, Nov 23 2016

Keywords

Links

Crossrefs

Inverse: A278503.
Cf. A278538, A278539.
Cf. also A278506, A278512.

Programs

  • Scheme
    (define (A278504 n) (let ((row (A278539 n)) (col (A278538 n))) (* (/ 1 2) (- (expt (+ row col) 2) row col col col -2))))

Formula

a(n) = (1/2) * ((c+r)^2 - r - 3*c + 2), where c = A278538(n), and r = A278539(n).

A278506 Inverse permutation to A278505.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 11, 9, 16, 8, 22, 10, 29, 14, 37, 12, 46, 15, 56, 13, 67, 17, 79, 20, 92, 21, 106, 23, 121, 27, 137, 18, 154, 30, 172, 19, 191, 28, 211, 38, 232, 35, 254, 24, 277, 47, 301, 36, 326, 26, 352, 57, 379, 25, 407, 31, 436, 68, 466, 44, 497, 45, 529, 80, 562, 54, 596, 39, 631, 93, 667, 34, 704, 32
Offset: 1

Views

Author

Antti Karttunen, Nov 23 2016

Keywords

Links

Crossrefs

Inverse: A278505.
Cf. A278538, A278539.
Cf. also A278504, A278512.

Programs

  • Scheme
    (define (A278506 n) (let ((row (A278538 n)) (col (A278539 n))) (* (/ 1 2) (- (expt (+ row col) 2) row col col col -2))))

Formula

a(n) = (1/2) * ((c+r)^2 - r - 3*c + 2), where c = A278539(n), and r = A278538(n).

A278511 Square array constructed from Flavius sieve, shifted version, read by descending antidiagonals.

Original entry on oeis.org

2, 4, 3, 6, 5, 7, 8, 11, 9, 13, 10, 17, 21, 15, 19, 12, 23, 33, 37, 25, 27, 14, 29, 45, 55, 51, 31, 39, 16, 35, 57, 75, 85, 73, 43, 49, 18, 41, 69, 97, 111, 121, 99, 61, 63, 20, 47, 81, 115, 145, 159, 151, 127, 67, 79, 22, 53, 93, 135, 171, 199, 211, 193, 163, 87, 91, 24, 59, 105, 157, 205, 243, 267, 271, 247, 187, 103, 109
Offset: 1

Views

Author

Antti Karttunen, Nov 23 2016

Keywords

Comments

Note how in comparison to A278505, the even numbers on the first row have been shifted one step left, "pushing" term 1 out of the array proper. This was done to obtain a better alignment with arrays like A083221 and A255127 associated with other sieves, from which one may then induce permutations by cross-referencing. (See also A255551.)

Examples

			The top left corner of the array:
   2,  4,   6,   8,  10,  12,  14,  16,  18,  20
   3,  5,  11,  17,  23,  29,  35,  41,  47,  53
   7,  9,  21,  33,  45,  57,  69,  81,  93, 105
  13, 15,  37,  55,  75,  97, 115, 135, 157, 175
  19, 25,  51,  85, 111, 145, 171, 205, 231, 265
  27, 31,  73, 121, 159, 199, 243, 283, 327, 367
  39, 43,  99, 151, 211, 267, 319, 379, 433, 487
  49, 61, 127, 193, 271, 343, 421, 483, 559, 631
  63, 67, 163, 247, 339, 427, 519, 607, 691, 793
  79, 87, 187, 303, 403, 523, 639, 739, 853, 963

Links

Crossrefs

Inverse: A278512.
Cf. A000960 (column 1, but with its initial 1 replaced by 2), A278505, A278507.
Cf. A278538 (row index of n), A278537 (column index of n).
Cf. A083221, A255127, A255551 (analogous arrays constructed from other sieves).

Programs

Formula

A(1,col) = 2*col; For row > 1, A(row,1) = A000960(row) if col = 1, otherwise, A(row,col) = A278507(row,col-1).
For all n > 1, A(A278538(n), A278537(n)) = n.
Showing 1-3 of 3 results.

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