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Square array constructed from Flavius sieve, shifted version, read by descending antidiagonals
4

%I #28 Jul 15 2020 06:19:00

%S 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,

%T 51,31,39,16,35,57,75,85,73,43,49,18,41,69,97,111,121,99,61,63,20,47,

%U 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

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

%C 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.)

%H Antti Karttunen, <a href="/A278511/b278511.txt">Table of n, a(n) for n = 1..10440</a> [the first 144 antidiagonals of the array; offset adapted by _Georg Fischer_, JUl 15 2020]

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>

%F A(1,col) = 2*col; For row > 1, A(row,1) = A000960(row) if col = 1, otherwise, A(row,col) = A278507(row,col-1).

%F For all n > 1, A(A278538(n), A278537(n)) = n.

%e The top left corner of the array:

%e 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

%e 3, 5, 11, 17, 23, 29, 35, 41, 47, 53

%e 7, 9, 21, 33, 45, 57, 69, 81, 93, 105

%e 13, 15, 37, 55, 75, 97, 115, 135, 157, 175

%e 19, 25, 51, 85, 111, 145, 171, 205, 231, 265

%e 27, 31, 73, 121, 159, 199, 243, 283, 327, 367

%e 39, 43, 99, 151, 211, 267, 319, 379, 433, 487

%e 49, 61, 127, 193, 271, 343, 421, 483, 559, 631

%e 63, 67, 163, 247, 339, 427, 519, 607, 691, 793

%e 79, 87, 187, 303, 403, 523, 639, 739, 853, 963

%o (Scheme)

%o (define (A278511 n) (if (<= n 1) n (A278511bi (A002260 (- n 1)) (A004736 (- n 1)))))

%o (define (A278511bi row col) (cond ((= 1 row) (+ col col)) ((= 1 col) (A000960 row)) (else (A278507bi row (- col 1)))))

%o ;; Code for A278507bi given in A278507.

%Y Inverse: A278512.

%Y Cf. A000960 (column 1, but with its initial 1 replaced by 2), A278505, A278507.

%Y Cf. A278538 (row index of n), A278537 (column index of n).

%Y Cf. A083221, A255127, A255551 (analogous arrays constructed from other sieves).

%K nonn,tabl

%O 1,1

%A _Antti Karttunen_, Nov 23 2016