A254100 -id:A254100 - cp's OEIS frontend

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.

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

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.

A302036 Ludic powers: numbers k such that A302031(k) < 2; numbers k such that A260739(k) is a power of 2.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 29, 31, 32, 37, 41, 43, 45, 47, 49, 53, 55, 61, 64, 67, 71, 73, 77, 83, 85, 89, 91, 93, 97, 101, 107, 109, 115, 119, 121, 127, 128, 131, 143, 145, 149, 151, 157, 161, 167, 173, 175, 179, 181, 189, 191, 193, 197, 205, 209, 211, 221, 223, 227, 229, 233, 235, 239, 247, 253, 256, 257

Offset: 1

Antti Karttunen, Apr 02 2018

nonn

An analog of A000961 for factorization process based on the Ludic sieve (A255127).

Numbers k for which A302031(k) < 2, or equally, for which A302034(k) = 1, or equally, for which A209229(A260739(k)) = 1.

Antti Karttunen, Table of n, a(n) for n = 1..3600
Index entries for sequences generated by sieves

Cf. A260739, A302031, A302034.
Cf. A000079, A003309, A254100 (subsequences).
Cf. also A000961, A302038, A302040.

for(n=1,257,if(A302031(n)<2,print1(n,","))); \\ See also code in A302031.

A302038 Semiludic numbers or "Ludic semiprimes": numbers n for which A302037(n) = 2.

Original entry on oeis.org

4, 6, 9, 10, 14, 15, 19, 22, 26, 27, 31, 34, 35, 39, 46, 50, 55, 58, 59, 63, 65, 73, 74, 75, 82, 86, 94, 95, 99, 101, 103, 106, 113, 122, 133, 134, 135, 142, 145, 147, 154, 155, 163, 166, 167, 171, 178, 182, 185, 187, 194, 203, 205, 214, 219, 230, 238, 242, 243, 245, 253, 254, 255, 262, 263, 269, 271, 279, 286, 293, 298, 299, 311

Offset: 1

Antti Karttunen, Apr 01 2018

nonn

An analog for A001358 based on the Ludic factorization (see A302032).

Antti Karttunen, Table of n, a(n) for n = 1..3953
Index entries for sequences generated by sieves

Cf. A003309, A255127, A302032, A302037.
Cf. A254100 (a subsequence).
Cf. also A001358, A302036.

k=0; for(n=1,512,if(2==A302037(n),k++;print1(n,","))); \\ Other code as in A302037.

cp's OEIS Frontend

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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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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A302036 Ludic powers: numbers k such that A302031(k) < 2; numbers k such that A260739(k) is a power of 2.

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PARI

A302038 Semiludic numbers or "Ludic semiprimes": numbers n for which A302037(n) = 2.

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PARI