A192505 -id:A192505 - cp's OEIS frontend

A192607 Nonludic numbers: complement of A003309.

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 19, 20, 21, 22, 24, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87

Offset: 1

Reinhard Zumkeller, Jul 05 2011

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A192505 (not ludic but prime), A192506 (neither ludic nor prime).

a192607 n = a192607_list !! (n-1)
a192607_list = filter ((== 0) . a192490) [1..]

a3309[nmax_] := a3309[nmax] = Module[{t = Range[2, nmax], k, r = {1}}, While[Length[t] > 0, k = First[t]; AppendTo[r, k]; t = Drop[t, {1, -1, k}]]; r];
nmax = 1000;
Complement[Range[nmax], a3309[nmax]] (* Jean-François Alcover, Dec 10 2021, after Ray Chandler in A003309 *)

A192490(a(n)) = 0.

A192506 Numbers that are neither ludic nor prime.

Original entry on oeis.org

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94

Offset: 1

Reinhard Zumkeller, Jul 05 2011

nonn

Intersection of A002808 and A192607; (1-A010051(a(n)))*(1-A192490(a(n)))=1;
a(n) = A091212(n) for n <= 60.
a(n) = A175526(n) for n <= 53. - Reinhard Zumkeller, Jul 12 2011
In other words, composite numbers that are nonludic. - Antti Karttunen, May 11 2015

Reinhard Zumkeller (first 1000 terms) & Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A257689 (complement, either ludic or prime), A192503 (ludic and prime), A192504 (ludic and nonprime), A192505 (nonludic and prime).
Cf. A010051, A192490, A002808, A192607.
a(n) differs from A091212(n) and A205783(n+1) for the first time at n=37, where a(37) = 55, while 55 is missing from both A091212 and A205783.
Differs from A175526 for the first time at n=54, where a(54) = 78, while A175526(54) = 77, a term which is missing from here.

a192506 n = a192506_list !! (n-1)
a192506_list = filter ((== 0) . a010051) a192607_list
(Scheme, with Antti Karttunen's IntSeq-library)
(define A192506 (MATCHING-POS 1 1 (lambda (n) (and (zero? (A192490 n)) (zero? (A010051 n))))))
;; Antti Karttunen, May 07 2015

a3309[nmax_] := a3309[nmax] = Module[{t = Range[2, nmax], k, r = {1}}, While[Length[t] > 0, k = First[t]; AppendTo[r, k]; t = Drop[t, {1, -1, k}]]; r];
ludicQ[n_, nmax_] /; 1 <= n <= nmax := MemberQ[a3309[nmax], n];
terms = 1000;
f[nmax_] := f[nmax] = Select[Range[nmax], !ludicQ[#, nmax] && !PrimeQ[#]&] // PadRight[#, terms]&;
f[nmax = terms];
f[nmax = 2 nmax];
While[f[nmax] != f[nmax/2], nmax = 2 nmax];
seq = f[nmax] (* Jean-François Alcover, Dec 10 2021, after Ray Chandler in A003309 *)

A276569 Numbers such that ludic factor of n (A272565) does not divide n.

Original entry on oeis.org

19, 31, 49, 59, 73, 79, 85, 101, 103, 109, 113, 133, 137, 139, 145, 151, 163, 167, 169, 191, 197, 199, 203, 205, 229, 241, 251, 253, 259, 263, 269, 271, 281, 289, 293, 295, 299, 311, 317, 319, 323, 343, 347, 349, 355, 367, 371, 373, 379, 385, 391, 401, 403, 409, 413, 439, 443, 449, 451, 457, 461, 469, 473, 479, 487, 491, 499

Offset: 1

Antti Karttunen, Sep 11 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..3200

Complement: A276568.
Cf. A272565, A276440.
Subsequence of A276437.
Cf. A192505 (a subsequence).

A257689 Numbers that are either ludic or prime.

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 115, 119, 121, 127, 131, 137, 139, 143, 149, 151, 157, 161, 163, 167, 173, 175, 179, 181, 191, 193, 197, 199, 209, 211, 221, 223, 227, 229, 233, 235, 239, 241, 247, 251, 257, 263, 265

Offset: 1

Antti Karttunen, May 07 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10181

Union of primes (A000040) and ludic numbers (A003309).
Cf. A192506 (complement, neither ludic nor prime), A192503 (ludic and prime), A192504 (ludic and nonprime), A192505 (nonludic and prime).
Differs from A206074(n-1), A186891(n) and A257688(n) for the first time at n=19, where a(19) = 59, while A206074(18) = A186891(19) = A257688(19) = 55, a term missing from here.
Differs from A257691 for the first time at n=24, where a(24) = 77, while A257691(24) = 79.

a3309[nmax_] := a3309[nmax] = Module[{t = Range[2, nmax], k, r = {1}}, While[Length[t] > 0, k = First[t]; AppendTo[r, k]; t = Drop[t, {1, -1, k}]]; r];
ludicQ[n_, nmax_] /; 1 <= n <= nmax := MemberQ[a3309[nmax], n];
terms = 1000;
f[nmax_] := f[nmax] = Select[Range[nmax], ludicQ[#, nmax] || PrimeQ[#]&] // PadRight[#, terms]&;
f[nmax = terms];
f[nmax = 2 nmax];
While[f[nmax] != f[nmax/2], nmax = 2 nmax];
seq = f[nmax] (* Jean-François Alcover, Dec 10 2021, after Ray Chandler in A003309 *)

A276440 a(n) = greatest ludic number (A003309) that divides n.

Original entry on oeis.org

1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, 2, 17, 3, 1, 5, 7, 11, 23, 3, 25, 13, 3, 7, 29, 5, 1, 2, 11, 17, 7, 3, 37, 2, 13, 5, 41, 7, 43, 11, 5, 23, 47, 3, 7, 25, 17, 13, 53, 3, 11, 7, 3, 29, 1, 5, 61, 2, 7, 2, 13, 11, 67, 17, 23, 7, 71, 3, 1, 37, 25, 2, 77, 13, 1, 5, 3, 41, 83, 7, 17, 43, 29, 11, 89, 5, 91, 23, 3, 47

Offset: 1

Antti Karttunen, Sep 11 2016

nonn

			a(19) = 1 as 19 is not a ludic number, but it is a prime, thus only ludic number that divides it is the very first one A003309(1) = 1.
a(589) = 1 also as 589 = 19*31 and both 19 and 31 are in A192505.

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for sequences generated by sieves

Cf. A003309, A192505, A272565, A276568, A276569.

Differs from A006530 for the first time at n=19.

(define (A276440 n) (let loop ((k 1) (mt 1)) (let ((t (A003309 k))) (cond ((> t n) mt) ((zero? (modulo n t)) (loop (+ 1 k) t)) (else (loop (+ 1 k) mt))))))

A276447 Numbers n for which A272565(n) < A020639(n).

Original entry on oeis.org

19, 31, 49, 59, 73, 79, 101, 103, 109, 113, 137, 139, 151, 163, 167, 169, 191, 197, 199, 229, 241, 251, 259, 263, 269, 271, 281, 289, 293, 299, 311, 317, 319, 323, 347, 349, 367, 373, 379, 391, 401, 409, 439, 443, 449, 451, 457, 461, 469, 479, 487, 491, 499, 521, 523, 529, 533, 547, 557, 559, 563, 569, 571, 583, 587, 589, 599, 601

Offset: 1

Antti Karttunen, Sep 11 2016

nonn

			19 is present as A272565(19)=5 and 5 < A020639(19)=19. (19 is right after 5 on the third row of array A255127 while on A083221 it occurs at the beginning of row 8 that starts with 19 itself).
49 is present as it occurs as the fourth number on the third row of A255127 beginning with 5: 5,  19,  35,  49, ..., thus A272565(49)=5, while in A083221 49 occurs right after 7 on row 4, thus A020639(49)=7, and 5 < 7.

Antti Karttunen, Table of n, a(n) for n = 1..2000

Cf. A276448 (complement in A276437), A276347.

Cf. A020639, A272565, A192505, A083221, A255127.

cp's OEIS Frontend

A192607 Nonludic numbers: complement of A003309.

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A192506 Numbers that are neither ludic nor prime.

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A276569 Numbers such that ludic factor of n (A272565) does not divide n.

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A257689 Numbers that are either ludic or prime.

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A276440 a(n) = greatest ludic number (A003309) that divides n.

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A276447 Numbers n for which A272565(n) < A020639(n).

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