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

%I A278511 #34 Aug 02 2025 06:52:09
%S A278511 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 A278511 51,31,39,16,35,57,75,85,73,43,49,18,41,69,97,111,121,99,61,63,20,47,
%U A278511 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 A278511 Square array constructed from Flavius sieve, shifted version, read by descending antidiagonals.
%C A278511 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 A278511 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 A278511 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%H A278511 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F A278511 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 A278511 For all n > 1, A(A278538(n), A278537(n)) = n.
%e A278511 The top left corner of the array:
%e A278511    2,  4,   6,   8,  10,  12,  14,  16,  18,  20
%e A278511    3,  5,  11,  17,  23,  29,  35,  41,  47,  53
%e A278511    7,  9,  21,  33,  45,  57,  69,  81,  93, 105
%e A278511   13, 15,  37,  55,  75,  97, 115, 135, 157, 175
%e A278511   19, 25,  51,  85, 111, 145, 171, 205, 231, 265
%e A278511   27, 31,  73, 121, 159, 199, 243, 283, 327, 367
%e A278511   39, 43,  99, 151, 211, 267, 319, 379, 433, 487
%e A278511   49, 61, 127, 193, 271, 343, 421, 483, 559, 631
%e A278511   63, 67, 163, 247, 339, 427, 519, 607, 691, 793
%e A278511   79, 87, 187, 303, 403, 523, 639, 739, 853, 963
%o A278511 (Scheme)
%o A278511 (define (A278511 n) (if (<= n 1) n (A278511bi (A002260 (- n 1)) (A004736 (- n 1)))))
%o A278511 (define (A278511bi row col) (cond ((= 1 row) (+ col col)) ((= 1 col) (A000960 row)) (else (A278507bi row (- col 1)))))
%o A278511 ;; Code for A278507bi given in A278507.
%Y A278511 Inverse: A278512.
%Y A278511 Cf. A000960 (column 1, but with its initial 1 replaced by 2), A278505, A278507.
%Y A278511 Cf. A278538 (row index of n), A278537 (column index of n).
%Y A278511 Cf. A083221, A255127, A255551 (analogous arrays constructed from other sieves).
%K A278511 nonn,tabl
%O A278511 1,1
%A A278511 _Antti Karttunen_, Nov 23 2016