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

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

1,1

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.)

Links

Antti Karttunen, Table of n, a(n) for n = 1..10440 [the first 144 antidiagonals of the array; offset adapted by Georg Fischer, JUl 15 2020]

Index entries for sequences generated by sieves

Index entries for sequences related to the Josephus Problem

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.

Example

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

Prog

(Scheme)
(define (A278511 n) (if (<= n 1) n (A278511bi (A002260 (- n 1)) (A004736 (- n 1)))))
(define (A278511bi row col) (cond ((= 1 row) (+ col col)) ((= 1 col) (A000960 row)) (else (A278507bi row (- col 1)))))
;; Code for A278507bi given in A278507.

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).

Sequence in context: A366943 A366945 A278512 * A255552 A255551 A366949

Adjacent sequences: A278508 A278509 A278510 * A278512 A278513 A278514

Keyword

nonn,tabl

Author

Antti Karttunen, Nov 23 2016

Status

approved