A255127 -id:A255127 - cp's OEIS frontend

A269379 a(1) = 1; for n > 1, a(n) = A255127(A260738(n)+1, A260739(n)).

1, 3, 5, 9, 7, 15, 11, 21, 19, 27, 13, 33, 17, 39, 35, 45, 23, 51, 31, 57, 49, 63, 25, 69, 29, 75, 65, 81, 37, 87, 55, 93, 79, 99, 59, 105, 41, 111, 95, 117, 43, 123, 47, 129, 109, 135, 53, 141, 85, 147, 125, 153, 61, 159, 73, 165, 139, 171, 103, 177, 67, 183, 155, 189, 113, 195, 71, 201, 169, 207, 77, 213, 101, 219, 185, 225, 83

Offset: 1

Antti Karttunen, Mar 01 2016

nonn

a(n) = the number located immediately below n in A255127 (square array generated by Ludic sieve) in the same column where n itself is, or in other words, the number removed in the next filtering stage at the same step as when n was removed in the A260738(n)-th stage.

Permutation of odd numbers.

Antti Karttunen, Table of n, a(n) for n = 1..32999

Cf. A255127, A260738, A260739.
Cf. A269171, A269356, A269358, A269382, A269385, A269387 (sequences that use this function).
Cf. A269380 (left inverse).
Cf. also A250469, A269369.

(define (A269379 n) (if (= 1 n) n (A255127bi (+ (A260738 n) 1) (A260739 n)))) ;; Code for A255127bi given in A255127.

a(1) = 1; for n > 1, a(n) = A255127(A260738(n)+1, A260739(n)).
Other identities. For all n >= 1:
A269380(a(n)) = n.

A255407 Permutation of natural numbers: a(n) = A255127(A252460(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 23, 20, 21, 22, 25, 24, 19, 26, 27, 28, 29, 30, 37, 32, 33, 34, 35, 36, 41, 38, 39, 40, 43, 42, 47, 44, 45, 46, 53, 48, 31, 50, 51, 52, 61, 54, 49, 56, 57, 58, 67, 60, 71, 62, 63, 64, 65, 66, 77, 68, 69, 70, 83, 72, 89, 74, 75, 76, 59, 78, 91, 80, 81

Offset: 1

Antti Karttunen, Feb 22 2015

nonn

a(n) tells which number in Ludic array A255127 is at the same position where n is in array A083221, the sieve of Eratosthenes. As both arrays have A005843 (even numbers) and A016945 as their two topmost rows, both sequences are among the fixed points of this permutation.

Equally: a(n) tells which number in array A255129 is at the same position where n is in the array A083140, as they are the transposes of above two arrays.

			A083221(8,1) = 19 and A255127(8,1) = 23, thus a(19) = 23.
A083221(9,1) = 23 and A255127(9,1) = 25, thus a(23) = 25.
A083221(3,2) = 25 and A255127(3,2) = 19, thus a(25) = 19.

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers

Cf. A001248, A003309, A007310, A008578, A083221, A084967, A252460, A254100, A255413, A255127.
Inverse: A255408.
Similar permutations: A249818.

a(n) = A255127(A252460(n)).
Other identities. For all n >= 1:
a(2n) = 2n. [Fixes even numbers.]
a(3n) = 3n. [Fixes multiples of three.]
a(A008578(n)) = A003309(n). [Maps noncomposites to Ludic numbers.]
a(A001248(n)) = A254100(n). [Maps squares of primes to "postludic numbers".]
a(A084967(n)) = a(5*A007310(n)) = A007310((5*n)-3) = A255413(n). [Maps A084967 to A255413.]
(And similarly between other columns and rows of A083221 and A255127.)

A260739 Column index to A255127: a(1) = 1; for n > 1, a(n) = the position at the stage where n is removed in the sieve which produces Ludic numbers.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 6, 1, 7, 3, 8, 1, 9, 2, 10, 4, 11, 1, 12, 1, 13, 5, 14, 1, 15, 2, 16, 6, 17, 3, 18, 1, 19, 7, 20, 1, 21, 1, 22, 8, 23, 1, 24, 4, 25, 9, 26, 1, 27, 2, 28, 10, 29, 3, 30, 1, 31, 11, 32, 5, 33, 1, 34, 12, 35, 1, 36, 2, 37, 13, 38, 1, 39, 6, 40, 14, 41, 1, 42, 4, 43, 15, 44, 1, 45, 1, 46, 16, 47, 7, 48, 1, 49, 17, 50, 2

Offset: 1

Antti Karttunen, Jul 30 2015

nonn

Ordinal transform of A272565 (Ludic factor), and also of A260738. - Antti Karttunen, Apr 03 2018

Antti Karttunen, Table of n, a(n) for n = 1..10105

Column index to array A255127.
Cf. A003309, A254100, A272565.
Cf. A260738 (corresponding row index).
Cf. A302035, A302036 (positions of terms that are powers of 2).
Cf. A078898, A246277, A260429, A260439 for column indices to other arrays similar to A255127.
Differs from A246277 (and also after the initial term from A078898) for the first time at n=19.

(define (A260739 n) (cond ((= 1 n) 1) ((even? n) (/ n 2)) (else (let searchrow ((row 2)) (let searchcol ((col 1)) (cond ((>= (A255127bi row col) n) (if (= (A255127bi row col) n) col (searchrow (+ 1 row)))) (else (searchcol (+ 1 col))))))))) ;; Code for A255127bi given in A255127.

Other identities. For all n >= 2:
a(A003309(n)) = 1. [In Ludic sieve each Ludic number (after 1) is the first among the numbers removed at stage k.]
a(A254100(n)) = 2.
A255127(A260738(n), a(n)) = n.
For n > 1, A001511(a(n)) = A302035(n). - Antti Karttunen, Apr 03 2018

Term a(1) changed from 0 to 1 to match with the definition of A078898 and the interpretation as an ordinal transform - Antti Karttunen, Apr 03 2018

A254100 Postludic numbers: Second column of Ludic array A255127.

Original entry on oeis.org

4, 9, 19, 31, 55, 73, 101, 145, 167, 205, 253, 293, 317, 355, 413, 473, 521, 569, 623, 677, 737, 763, 833, 917, 983, 1027, 1051, 1121, 1171, 1273, 1337, 1411, 1471, 1571, 1619, 1663, 1681, 1807, 1957, 1991, 2087, 2113, 2171, 2245, 2275, 2335, 2401, 2497, 2593, 2713, 2771, 2831, 2977, 3047, 3113

Offset: 1

Antti Karttunen, Feb 22 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10001

Column 2 of A255127. (Row 2 of A255129). Positions of 2's in A260739.
Subsequence of A192607, A302036 and A302038.
Cf. A276576, A276606 (first differences).
Cf. also A001248, A219178.

rows = 100; cols = 2; t = Range[2, 10^4]; r = {1}; n = 1; While[n <= rows, k = First[t]; AppendTo[r, k]; t0 = t; t = Drop[t, {1, -1, k}]; ro[n++] = Complement[t0, t][[1 ;; cols]]]; A = Array[ro, rows]; Table[A[[n, 2]], {n, 1, rows} ] (* Jean-François Alcover, Mar 14 2016, after Ray Chandler *)

(define (A254100 n) (A255127bi n 2)) ;; A255127bi given in A255127.

a(n) = A255407(A001248(n)).

A260738 Row index to A255127: a(1) = 0; for n > 1, a(n) = number of the stage where n is removed in the sieve which produces Ludic numbers.

Original entry on oeis.org

0, 1, 2, 1, 3, 1, 4, 1, 2, 1, 5, 1, 6, 1, 2, 1, 7, 1, 3, 1, 2, 1, 8, 1, 9, 1, 2, 1, 10, 1, 4, 1, 2, 1, 3, 1, 11, 1, 2, 1, 12, 1, 13, 1, 2, 1, 14, 1, 3, 1, 2, 1, 15, 1, 5, 1, 2, 1, 4, 1, 16, 1, 2, 1, 3, 1, 17, 1, 2, 1, 18, 1, 6, 1, 2, 1, 19, 1, 3, 1, 2, 1, 20, 1, 4, 1, 2, 1, 21, 1, 22, 1, 2, 1, 3, 1, 23, 1, 2, 1, 7, 1, 5, 1, 2, 1, 24, 1, 3, 1, 2, 1, 4, 1, 25, 1, 2, 1, 26, 1

Offset: 1

Antti Karttunen, Jul 30 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10105

Row index to array A255127.
Cf. A003309, A254100.
Cf. A260739 (corresponding column index).
Cf. A055396, A260438 for row indices to other arrays similar to A255127.
Differs from A055396 for the first time at n=19.

(define (A260738 n) (cond ((= 1 n) 0) ((even? n) 1) (else (let searchrow ((row 2)) (let searchcol ((col 1)) (cond ((>= (A255127bi row col) n) (if (= (A255127bi row col) n) row (searchrow (+ 1 row)))) (else (searchcol (+ 1 col))))))))) ;; Code for A255127bi given in A255127.

Other identities. For all n >= 1:
a(A003309(n)) = n-1. [In Ludic sieve A003309(k+1) (i.e., the k-th Ludic number after 1) is the first among the numbers removed at stage k.]
a(2n) = 1. [All even numbers are removed at the stage one of the sieve.]
a(A016945(n)) = 2, a(A255413(n)) = 3, a(A255414(n)) = 4, ..., a(A255419(n)) = 9.
a(A254100(n)) = n.
For all n >= 2:
A255127(a(n), A260739(n)) = n.

A260741 Permutation of natural numbers: a(1) = 1, for n > 1: a(n) = A255127(A260438(n), a(A260439(n))).

Original entry on oeis.org

1, 2, 3, 4, 9, 6, 5, 8, 7, 18, 15, 12, 11, 10, 13, 16, 21, 14, 19, 36, 17, 30, 51, 24, 23, 22, 31, 20, 33, 26, 25, 32, 29, 42, 27, 28, 37, 38, 35, 72, 45, 34, 41, 60, 55, 102, 39, 48, 43, 46, 47, 44, 105, 62, 73, 40, 59, 66, 87, 52, 49, 50, 53, 64, 69, 58, 61, 84, 67, 54, 63, 56, 71, 74, 77, 76, 57, 70, 83, 144, 125, 90, 75, 68, 101, 82, 89, 120

Offset: 1

Antti Karttunen, Jul 30 2015

nonn

This is a more recursed variant of A260435.

Antti Karttunen, Table of n, a(n) for n = 1..10104
Index entries for sequences that are permutations of the natural numbers

Inverse: A260742.
Cf. A000959, A003309, A255127, A260438, A260439.
Similar permutations: A260435, A250245, A250246.

a(1) = 1, for n > 1: a(n) = A255127(A260438(n), a(A260439(n))).
Other identities. For all n >= 1:
a(A000959(n+1)) = A003309(n+2). [Maps Lucky numbers to odd Ludic numbers.]
a(n) = a(2n)/2. [The even bisection halved gives the sequence back.]

A302032 Discard the least ludic factor of n: a(n) = A255127(A260738(c) + r - 1, A260739(c)), where r = A260738(n), c = A260739(n) are the row and the column index of n in the table A255127; a(n) = 1 if c = 1.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 5, 8, 1, 9, 5, 10, 9, 11, 1, 12, 1, 13, 7, 14, 1, 15, 7, 16, 15, 17, 7, 18, 1, 19, 11, 20, 1, 21, 1, 22, 21, 23, 1, 24, 19, 25, 19, 26, 1, 27, 11, 28, 27, 29, 11, 30, 1, 31, 13, 32, 11, 33, 1, 34, 33, 35, 1, 36, 13, 37, 17, 38, 1, 39, 35, 40, 39, 41, 1, 42, 31, 43, 35, 44, 1, 45, 1, 46, 45, 47, 13, 48, 1, 49, 23, 50

Offset: 1

Antti Karttunen, Mar 31 2018

nonn

Original definition: A032742 analog for a nonstandard factorization process based on the Ludic sieve (A255127); Discard a single instance of the Ludic factor A272565(n) from n.
Like [A020639(n), A032742(n)] or [A020639(n), A302042(n)], also ordered pair [A272565(n), a(n)] is unique for each n. Iterating n, a(n), a(a(n)), a(a(a(n))), ..., until 1 is reached, and taking the Ludic factor (A272565) of each term gives a multiset of Ludic numbers (A003309) in ascending order, unique for each natural number n >= 1. Permutation pair A302025/A302026 maps between this "Ludic factorization" and the ordinary prime factorization of n. See also comments in A302034.
The definition of "discard the least ludic factor" is based on the table A255127 of the ludic sieve, where row r lists the (r+1)-th ludic number k = A003309(r+1), determined at the r-th step of the sieve, followed by the numbers crossed out at this step, namely, every k-th of the numbers remaining so far after k. If the number n is in  row r = A260738(n), column c = A260739(n) of that table, then its least ludic factor is A272565(n) = A003309(r+1), the 1st entry of the r-th row. To discard that factor means to consider the number which is r-1 rows below the number c in that table, whence a(n) = A255127(A260738(c)+r-1, A260739(c)) - unless n is a ludic number, in which case a(n) = 1. - M. F. Hasler, Nov 06 2024

			Frem _M. F. Hasler_, Nov 06 2024: (Start)
For ludic numbers 1, 2, 3, 5, 7, 11, 13, 17, 23, 25, 29, 37, ..., a(n) = 1.
For n = 4, an even number, we have r = A260738(4) = 1: It is listed in row 1 of the table A255127, which lists all numbers that were crossed out at the first step: namely, the ludic number k = 2 and every other larger number. Also, in this row 1, the number 4 is in column c = A260739(4) = 2. Therefore, we apply r-1 = 0 times the map A269379 to c = 2, whence a(4) = 2.
The number n = 6 is also even and therefore listed in row r = 1, now in column c = 3, whence a(6) = 3. Similarly, a(8) = 4 and a(2k) = k for all k >= 1.
The number n = 9 was crossed out at the 2nd step (so r = A260738(9) = 2), when k = 3 was added to the ludic numbers and every 3rd remaining number crossed out; 9 was the first of these (after k = 3) so it is in column c = A260739(9) = 2. Now we have to apply r-1 = 1 times the map A269379 to c. That map yields the number which is located just below the argument (here c = 2) in the table A255127. Since 2 is a ludic number, in the first column, we get the next larger ludic number, 3, whence a(9) = 3.
The number 15 was the (c = 3)rd number to be crossed out at the (r = 2)nd step. Hence a(15) = A269379^{r-1} (c) = A269379(3) = 5 (again, the next larger ludic number).
The number 19 was the (c = 2)nd number to be crossed out at the (r = 3)rd step (when k = 5, its least ludic factor, was added to the list of ludic numbers). Hence a(19) = A269379^2(2) = A269379(3) = 5 again (skipping twice to the next larger ludic number).
(End)
To illustrate how this sequence allows one to compute the complete "ludic factorization" of a number, we consider n = 100.
For n = 100, its Ludic factor A272565(100) is 2, and we have seen that a(n) = 100/2 = 50.
For n = 50, its Ludic factor A272565(50) is 2 again, and again a(50) = 50/2 = 25.
Since n = 25 = A003309(1+9) is a ludic number, it equals its Ludic factor A272565(25) = 25. Because it appeared at the A260738(25) = 9th step, we apply A269379 eight times to the column index A260739(25) = 1, a fixed point, so a(25) = A269379^8(1) = 1.
Collecting the Ludic factors given by A272565 we get the multiset of factors: [2, 2, 25] = [A003309(1+1), A003309(1+1), A003309(1+9)]. By definition, A302026(100) = prime(1)*prime(1)*prime(9) = 2*2*23 = 92, the product of the corresponding primes.
If we start from n = 100, iterating the map n -> A302034(n) [instead of A302032] and apply A272565 to each term obtained we get just a single instance of each Ludic factor: [2, 25]. Then by applying A302035 to the same terms we get the corresponding exponents (multiplicities) of those factors: [2, 1].

Antti Karttunen, Table of n, a(n) for n = 1..32768
Index entries for sequences generated by sieves

Cf. A003309, A255127, A269379, A269380, A272565, A260738, A260739, A269379, A269380, A302025, A302026, A302034, A302035.
Cf. the following analogs A302031 (omega), A302037 (bigomega).
Cf. also A032742, A302042.

\\ Assuming A269379 and its inverse A269380 have been precomputed, then the following is reasonably fast:
A302032(n) = if(1==n,n,my(k=0); while((n%2), n = A269380(n); k++); n = n/2; while(k>0, n = A269379(n); k--); (n))

For n > 1, a(n) = A269379^r'(A260739(n)), where r' = A260738(n)-1 and A269379^r'(n) stands for applying r' times the map x -> A269379(x), starting from x = n.
a(n) = A302025(A032742(A302026(n))).
From M. F. Hasler, Nov 06 2024: (Start)
a(n) = 1 if n is a ludic number, i.e., in A003309. Otherwise:
a(n) = A255127(A260738(c) + r - 1, A260739(c)), with r = A260738(n), c = A260739(n).
In particular, a(2n) = n for all n. (End)

A255413 a(n) = 15*n - 11 + (n mod 2). Row 3 of Ludic array A255127.

Original entry on oeis.org

5, 19, 35, 49, 65, 79, 95, 109, 125, 139, 155, 169, 185, 199, 215, 229, 245, 259, 275, 289, 305, 319, 335, 349, 365, 379, 395, 409, 425, 439, 455, 469, 485, 499, 515, 529, 545, 559, 575, 589, 605, 619, 635, 649, 665, 679, 695, 709, 725, 739, 755, 769, 785, 799, 815, 829, 845, 859, 875, 889, 905, 919, 935, 949, 965, 979, 995, 1009

Offset: 1

Antti Karttunen, Feb 22 2015

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Row 3 of A255127.

Cf. A007310, A016921, A084967, A255407.

a[n_] := 15 n + Mod[n, 2] - 11;
Array[a, 100] (* Jean-François Alcover, Mar 14 2016 *)

apply( {A255413(n)=15*n-11+n%2}, [1..50]) \\ M. F. Hasler, Nov 09 2024

;; two alternatives:
(define (A255413 n) (A255127bi 3 n)) ;; Code for A255127bi given in A255127.
(define (A255413 n) (A007310 (- (* 5 n) 3)))

a(n) = A007310((5*n)-3).
a(n) = A255407(A084967(n)) = A255407(5*A007310(n)).
a(2n+1) = 5*A016921(n) for all n >= 0.
From M. F. Hasler, Nov 09 2024: (Start)
a(n) = a(n-1) + a(n-2) + a(n-3) for n > 3, a(1..3) = (5, 19, 35).
a(n) = a(n-2) + 30 for n > 2, with a(1..2) = (5, 19).
a(2n-1) = 30n - 25, a(2n) = 30n - 11.
G.f.: x*(5 + 14*x + 11*x^2)/((1 - x)^2*(1 + x)). (End)
E.g.f.: 11 + (15*x - 11)*cosh(x) + 5*(3*x - 2)*sinh(x). - Stefano Spezia, Nov 12 2024

New definition from M. F. Hasler, Nov 09 2024

A255414 Row 4 of Ludic array A255127.

Original entry on oeis.org

7, 31, 59, 85, 113, 137, 163, 191, 217, 241, 269, 295, 323, 347, 373, 401, 427, 451, 479, 505, 533, 557, 583, 611, 637, 661, 689, 715, 743, 767, 793, 821, 847, 871, 899, 925, 953, 977, 1003, 1031, 1057, 1081, 1109, 1135, 1163, 1187, 1213, 1241, 1267, 1291, 1319, 1345, 1373, 1397, 1423, 1451, 1477, 1501, 1529, 1555, 1583, 1607, 1633, 1661

Offset: 1

Antti Karttunen, Feb 22 2015

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Row 4 of A255127.

Cf. A084968, A255407.

appy( {A255414(n)=(n--)\8*210+[7, 31, 59, 85, 113, 137, 163, 191][n%8+1]}, [1..30]) \\ M. F. Hasler, Nov 09 2024

(define (A255414 n) (A255127bi 4 n)) ;; Code for A255127bi given in A255127.

a(n) = A255407(A084968(n)).
From M. F. Hasler, Nov 09 2024: (Start)
a(n) = a(n-8) + 210 = 210*floor((n-1)/8) + a((n-1)%8 + 1), where % is the modulo or remainder operation.
a(n) = a(n-1) + a(n-8) - a(n-9) for n > 9, with a(1..9) given in DATA.
G.f.: x*(7 + 24*x + 28*x^2 + 26*x^3 + 28*x^4 + 24*x^5 + 26*x^6 + 28*x^7 + 19*x^8)/D with D = 1 - x - x^8 + x^9 = (1 + x^4)(1 - x^4) = (1 + x^4)(1 + x^2)(1 + x)(1 - x). (End)

A257257 Square array A(row,col) = A255127(row,col+1) - A255127(row,col): the first differences of each row of Ludic array.

Original entry on oeis.org

2, 2, 6, 2, 6, 14, 2, 6, 16, 24, 2, 6, 14, 28, 44, 2, 6, 16, 26, 48, 60, 2, 6, 14, 28, 48, 60, 84, 2, 6, 16, 24, 52, 64, 86, 122, 2, 6, 14, 26, 48, 66, 94, 126, 142, 2, 6, 16, 28, 48, 62, 86, 132, 144, 176, 2, 6, 14, 26, 44, 60, 94, 120, 146, 166, 216, 2, 6, 16, 24, 48, 64, 86, 132, 142, 180, 234, 252

Offset: 1

Antti Karttunen, Apr 19 2015

The array A(row,col) is read by downwards antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

			The top left corner of the array:
    2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2,   2
    6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6,   6
   14,  16,  14,  16,  14,  16,  14,  16,  14,  16,  14,  16,  14,  16,  14
   24,  28,  26,  28,  24,  26,  28,  26,  24,  28,  26,  28,  24,  26,  28
   44,  48,  48,  52,  48,  48,  44,  48,  52,  48,  48,  48,  44,  52,  48
   60,  60,  64,  66,  62,  60,  64,  62,  60,  70,  60,  60,  62,  64,  60
   84,  86,  94,  86,  94,  86,  82,  92,  88,  92,  88,  90,  90,  84,  90
  122, 126, 132, 120, 132, 126, 130, 126, 120, 132, 128, 126, 130, 128, 126
  142, 144, 146, 142, 146, 138, 150, 148, 140, 148, 146, 138, 150, 138, 150
  176, 166, 180, 168, 176, 178, 170, 178, 170, 180, 174, 172, 176, 178, 176
  216, 234, 226, 242, 228, 226, 240, 218, 234, 246, 220, 230, 234, 226, 234
  252, 270, 254, 274, 258, 254, 258, 276, 262, 266, 258, 256, 264, 276, 264
  274, 284, 268, 284, 304, 270, 282, 278, 294, 282, 282, 276, 282, 288, 292
  308, 316, 314, 316, 320, 316, 312, 308, 324, 336, 316, 302, 316, 314, 322
  360, 360, 354, 368, 360, 372, 370, 368, 352, 360, 380, 354, 370, 380, 352
  412, 434, 424, 420, 426, 440, 426, 420, 432, 424, 422, 444, 424, 422, 430
  ...

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of the array

Column 1: A256482.
Cf. A255127.
Cf. A257258 (same array but with terms divided by 2).
Cf. also arrays A257251 and A257255.

(define (A257257 n) (A257257bi (A002260 n) (A004736 n)))
(define (A257257bi row col) (- (A255127bi row (+ 1 col)) (A255127bi row col))) ;; Code for A255127bi given in A255127.

A(row,col) = A255127(row,col+1) - A255127(row,col).

A(row,col) = 2*A257258(row,col).

cp's OEIS Frontend

A269379 a(1) = 1; for n > 1, a(n) = A255127(A260738(n)+1, A260739(n)).

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A255407 Permutation of natural numbers: a(n) = A255127(A252460(n)).

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A260739 Column index to A255127: a(1) = 1; for n > 1, a(n) = the position at the stage where n is removed in the sieve which produces Ludic numbers.

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A254100 Postludic numbers: Second column of Ludic array A255127.

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A260738 Row index to A255127: a(1) = 0; for n > 1, a(n) = number of the stage where n is removed in the sieve which produces Ludic numbers.

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A260741 Permutation of natural numbers: a(1) = 1, for n > 1: a(n) = A255127(A260438(n), a(A260439(n))).

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A302032 Discard the least ludic factor of n: a(n) = A255127(A260738(c) + r - 1, A260739(c)), where r = A260738(n), c = A260739(n) are the row and the column index of n in the table A255127; a(n) = 1 if c = 1.

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A255413 a(n) = 15*n - 11 + (n mod 2). Row 3 of Ludic array A255127.

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