A050435 -id:A050435 - cp's OEIS frontend

A076236 a(n) = A050435(n) mod A002808(n).

1, 0, 7, 7, 8, 9, 10, 10, 10, 10, 12, 12, 12, 12, 13, 13, 13, 14, 15, 16, 16, 16, 16, 16, 17, 17, 17, 18, 19, 19, 19, 20, 20, 20, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 26, 26, 27, 28, 28, 28, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 32

Offset: 1

Labos Elemer, Oct 08 2002

nonn

Original name: Remainder when 2nd order composite, A050435(n), is divided by first order composite, A002808(n). - Michael De Vlieger, Dec 09 2018

			Let c(n) be the n-th composite number. a(1) = 1 since c(c(1)) mod c(1) = c(4) mod 4 = 9 mod 4 = 1. a(2) = 0 since c(c(2)) mod c(2) = c(6) mod 6 = 12 mod 6 = 0. - _Michael De Vlieger_, Dec 09 2018

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A002808, A050435-A050439, A065860, A076237-A076239.

c[n_] := FixedPoint[n + PrimePi[#] + 1 &, n + PrimePi[n] + 1]; Array[Mod[c@ c@ #, c@ #] &, 71] (* Michael De Vlieger, Dec 09 2018, after Robert G. Wilson v at A002808 *)

a(n) = A050435(n) mod A002808(n).

Edited by Michael De Vlieger, Dec 09 2018

A076237 a(n) = A050435(n) mod n.

Original entry on oeis.org

0, 0, 0, 0, 3, 3, 3, 1, 8, 8, 10, 9, 8, 8, 8, 7, 6, 6, 7, 8, 7, 6, 5, 4, 5, 4, 3, 4, 5, 4, 3, 4, 3, 2, 2, 2, 2, 1, 0, 0, 40, 0, 0, 43, 43, 44, 44, 45, 45, 45, 47, 48, 49, 50, 50, 50, 53, 53, 53, 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, 56, 57, 58, 59, 59, 60, 62, 63, 63, 64, 65, 65, 65, 67

Offset: 1

Labos Elemer, Oct 08 2002

nonn

Cf. A002808, A050435-A050439, A065860, A076236-A076239.

Module[{cmps=Select[Range[300],CompositeQ],c2},c2=Table[cmps[[cmps[[n]]]],{n,100}];Mod[#[[1]],#[[2]]]&/@Thread[{c2,Range[Length[c2]]}]] (* Harvey P. Dale, May 02 2022 *)

a(n) = Mod[cc[n], n] = Mod[A050435(n), n]

A022449 c(p(n)) where p(k) is k-th prime including p(1)=1 and c(k) is k-th composite number.

Original entry on oeis.org

4, 6, 8, 10, 14, 20, 22, 27, 30, 35, 44, 46, 54, 58, 62, 66, 75, 82, 85, 92, 96, 99, 108, 114, 120, 129, 134, 136, 142, 144, 148, 166, 171, 178, 182, 194, 196, 204, 210, 215, 221, 230, 232, 245, 247, 252, 254, 268, 285, 289, 291, 296, 302, 304, 318

Offset: 1

Clark Kimberling

nonn

a(n) U A050435(n) = A002808(n), a(n+1) U A175251(n) = A002808(n) for n >= 1. a(n) = A065858(n-1) = composites (A002808) with prime (A000040) subscripts for n >=2. [From Jaroslav Krizek, Mar 13 2010]

			a(5) = 14 because a(5) = composite(noncomposite(5)) = composite(7) =14. _Jaroslav Krizek_, Mar 13 2010

C. Kimberling, Fractal sequences and interspersions, Ars Combinatoria, vol. 45 p 157 1997.

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

A065858 with a leading 4.

a022449 = a002808 . a008578
a022449_list = map a002808 a008578_list
-- Reinhard Zumkeller, Jan 12 2013

A022449 := proc(n)
    A002808(A008578(n)) ;
end proc:
seq(A022449(n),n=1..40) ; # R. J. Mathar, Jan 28 2014

p[1] = 1; p[n_] := Prime[n - 1];
Composite[n_] := FixedPoint[n + PrimePi[#] + 1 & , n + PrimePi[n] + 1];
a[n_] := Composite[p[n]];
Array[a, 100] (* Jean-François Alcover, Jan 26 2018, after Robert G. Wilson v *)

a(n) = A002808(A008578(n)). - Jaroslav Krizek, Mar 13 2010

Definition corrected by Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Mar 30 2005

A050439 Fifth-order composites.

Original entry on oeis.org

39, 49, 55, 56, 60, 69, 74, 77, 78, 84, 93, 94, 95, 100, 105, 106, 110, 115, 119, 124, 125, 126, 130, 133, 140, 141, 145, 152, 155, 156, 159, 162, 164, 165, 170, 174, 180, 183, 184, 188, 189, 198, 201, 202, 203, 206, 207, 209, 212, 213, 218, 222, 225, 231

Offset: 1

Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999

			C(C(C(C(C(8))))) = C(C(C(C(15)))) = C(C(C(25))) = C(C(38)) = C(55) = 77. So 77 is in the sequence.

N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A049076-A049081, A006450, A050435, A050436, A050438, A050440.

C := remove(isprime,[$4..1000]): seq(C[C[C[C[C[n]]]]],n=1..100);

Let C(n) be the n-th composite number, with C(1)=4. Then these are numbers C(C(C(C(C(n))))).

More terms from Asher Auel Dec 15 2000

A050436 Third-order composites.

Original entry on oeis.org

16, 21, 25, 26, 28, 33, 36, 38, 39, 42, 48, 49, 50, 52, 55, 56, 57, 60, 64, 68, 69, 70, 72, 74, 77, 78, 80, 84, 87, 88, 90, 93, 94, 95, 98, 100, 104, 105, 106, 110, 111, 115, 117, 118, 119, 121, 122, 124, 125, 126, 130, 133, 135, 138, 140, 141, 145, 146, 147

Offset: 1

Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999

			C(C(C(8))) = C(C(15)) = C(25) = 38. So 38 is in the sequence.

N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A049076, A049077, A049078, A049079, A049080, A049081, A006450, A050435, A050438, ...

C := remove(isprime,[$4..1000]): seq(C[C[C[C[n]]]],n=1..100);

Nest[Values@ KeySelect[MapIndexed[First@ #2 -> #1 &, #], CompositeQ] &, Select[Range@ 150, CompositeQ], 2] (* Michael De Vlieger, Jul 22 2017 *)

Let C(n) be the n-th composite number, with C(1)=4. Then these are numbers C(C(C(n))).

More terms from Asher Auel Dec 15 2000

A050438 Fourth-order composites.

Original entry on oeis.org

26, 33, 38, 39, 42, 49, 52, 55, 56, 60, 68, 69, 70, 74, 77, 78, 80, 84, 88, 93, 94, 95, 98, 100, 105, 106, 110, 115, 118, 119, 121, 124, 125, 126, 130, 133, 138, 140, 141, 145, 146, 152, 154, 155, 156, 159, 160, 162, 164, 165, 170, 174, 176, 180, 183, 184

Offset: 1

Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999

			C(C(C(C(8)))) = C(C(C(15))) = C(C(25)) = C(38) = 55. So 55 is in the sequence.

N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A049076-A049081, A006450, A050435, A050436, A050439, A050440.

C := remove(isprime,[$4..1000]): seq(C[C[C[C[n]]]],n=1..100);

Let C(n) be the n-th composite number, with C(1)=4. Then these are numbers C(C(C(C(n)))).

More terms from Asher Auel Dec 15 2000

A076239 Remainder when 3rd-order composite ccc(n) = A050436(n) is divided by n.

Original entry on oeis.org

0, 1, 1, 2, 3, 3, 1, 6, 3, 2, 4, 1, 11, 10, 10, 8, 6, 6, 7, 8, 6, 4, 3, 2, 2, 0, 26, 0, 0, 28, 28, 29, 28, 27, 28, 28, 30, 29, 28, 30, 29, 31, 31, 30, 29, 29, 28, 28, 27, 26, 28, 29, 29, 30, 30, 29, 31, 30, 29, 32, 31, 30, 29, 28, 29, 28, 27, 26, 26, 25, 26, 26, 26, 26, 26, 28, 29

Offset: 1

Labos Elemer, Oct 08 2002

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A002808, A050435, A050436, A050438, A050439.

Cf. A065860, A076236, A076237, A076238.

MapIndexed[Mod[#1, First@ #2] &, #] &@ Nest[Values@ KeySelect[ MapIndexed[ First@ #2 -> #1 &, #], CompositeQ] &, Select[Range@ 183, CompositeQ], 2] (* Michael De Vlieger, Jul 22 2017 *)

a(n) = ccc(n) mod n = A050436(n) mod n.

A175251 Composites (A002808) with nonprime (A018252) subscripts.

Original entry on oeis.org

4, 9, 12, 15, 16, 18, 21, 24, 25, 26, 28, 32, 33, 34, 36, 38, 39, 40, 42, 45, 48, 49, 50, 51, 52, 55, 56, 57, 60, 63, 64, 65, 68, 69, 70, 72, 74, 76, 77, 78, 80, 81, 84, 86, 87, 88, 90, 91, 93, 94, 95, 98, 100

Offset: 1

Jaroslav Krizek, Mar 13 2010

nonn

a(n) = composite(nonprime(n)) = A002808(A018252(n)). a(n) U A065858(n) = A002808(n), a(n+1) U A022449(n) = A002808(n) for n >= 1. a(1) = 4, a(n) = A050435(n-1) = composites (A002808) with composite (A002808) subscripts for n >=2.

			a(5) = 16 because a(5) = c(b(5)) = c(9) = 16, c = composite, b = nonprime.

A050440 Sixth-order composites.

Original entry on oeis.org

56, 69, 77, 78, 84, 94, 100, 105, 106, 115, 124, 125, 126, 133, 140, 141, 145, 152, 156, 162, 164, 165, 170, 174, 183, 184, 188, 198, 202, 203, 206, 209, 212, 213, 218, 222, 231, 235, 236, 242, 243, 253, 256, 258, 259, 262, 264, 266, 270, 272, 278, 284

Offset: 1

Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999

			C(C(C(C(C(C(1)))))) = C(C(C(C(C(4))))) = C(C(C(C(9)))) = C(C(C(16))) = C(C(26)) = C(39) = 56. So 56 is in the sequence. So 77 is in the sequence.

N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Cf. A049076-A049081, A006450, A050435, A050436, A050438, A050439.

C := remove(isprime,[$4..1000]): seq(C[C[C[C[C[C[n]]]]]],n=1..100);

Let C(n) be the n-th composite number, with C(1)=4. Then these are numbers C(C(C(C(C(C(n)))))).

More terms from Asher Auel Dec 15 2000

A076238 a(n) = A050436(n) mod A002808(n).

Original entry on oeis.org

0, 3, 1, 8, 8, 9, 8, 8, 7, 6, 8, 7, 6, 4, 5, 4, 3, 4, 4, 4, 3, 2, 2, 2, 1, 0, 0, 0, 43, 43, 44, 45, 45, 45, 47, 48, 50, 50, 50, 53, 53, 55, 55, 55, 55, 56, 56, 56, 56, 56, 58, 59, 60, 62, 63, 63, 65, 65, 65, 68, 68, 68, 68, 68, 69, 69, 69, 69, 70, 70, 72, 72, 73, 74, 74, 76, 78, 78

Offset: 1

Labos Elemer, Oct 08 2002

nonn

Cf. A002808, A050435-A050439, A065860, A076236-A076239.

a(n)=Mod[ccc[n], c[n]]=Mod[A050436(n), A002808[n]]

cp's OEIS Frontend

A076236 a(n) = A050435(n) mod A002808(n).

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A076237 a(n) = A050435(n) mod n.

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A022449 c(p(n)) where p(k) is k-th prime including p(1)=1 and c(k) is k-th composite number.

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A050439 Fifth-order composites.

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A050436 Third-order composites.

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A050438 Fourth-order composites.

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A076239 Remainder when 3rd-order composite ccc(n) = A050436(n) is divided by n.

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A175251 Composites (A002808) with nonprime (A018252) subscripts.