cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

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

Views

Author

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

Keywords

Examples

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

Links

Crossrefs

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

Programs

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

Formula

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

Extensions

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

Views

Author

Labos Elemer, Oct 08 2002

Keywords

Links

Crossrefs

Cf. A002808, A050435, A050436, A050438, A050439.
Cf. A065860, A076236, A076237, A076238.

Programs

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

Formula

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

A064812 Smallest prime p such that the infinite sequence {p, p'=2p-1, p''=2p'-1, ...} begins with a string of exactly n primes.

Original entry on oeis.org

5, 3, 2, 2131, 1531, 33301, 16651, 15514861, 857095381, 205528443121, 1389122693971, 216857744866621, 758083947856951, 107588900851484911, 69257563144280941
Offset: 1

Views

Author

David Terr, Oct 21 2002

Keywords

Comments

Chains of length n of nearly doubled primes.
Smallest prime beginning a complete Cunningham chain of length n of the second kind. (For the first kind see A005602.) - Jonathan Sondow, Oct 30 2015

Examples

			a(3) = 2 because 2 is the smallest prime such that the sequence {2, 3, 5, 9, ...} begins with exactly 3 primes, where each term in the sequence is twice the preceding term minus 1.

Links

Crossrefs

A better version of A005603.
Cf. (A005382 and A005383), A057326, A057327, A057328, A057329, A057330, A005602.
Cf. A002808, A006450, A049076-A049081, A050436, A076237-A076239, A050436-A050439, A065860, A181697, A263879.

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

Original entry on oeis.org

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

Views

Author

Labos Elemer, Oct 08 2002

Keywords

Comments

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

Examples

			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

Links

Crossrefs

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

Programs

Formula

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

Extensions

Edited by Michael De Vlieger, Dec 09 2018

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

Views

Author

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

Keywords

Examples

			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.

Links

Crossrefs

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

Programs

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

Formula

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

Extensions

More terms from Asher Auel Dec 15 2000

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

Views

Author

Labos Elemer, Oct 08 2002

Keywords

Crossrefs

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

Programs

  • Mathematica
    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 *)

Formula

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

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

Views

Author

Labos Elemer, Oct 08 2002

Keywords

Crossrefs

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

Formula

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

A260621 Let b(k, n) = number obtained when the map x->A002808(x) is applied k times to n; a(n) is the smallest k such that b(k, n) + 1 is prime.

Original entry on oeis.org

1, 1, 12, 2, 1, 1, 3, 11, 1, 1, 7, 9, 1, 2, 10, 4, 2, 1, 1, 6, 8, 3, 3, 1, 9, 3, 1, 1, 18, 3, 1, 5, 7, 2, 2, 1, 4, 8, 2, 14, 1, 1, 6, 17, 2, 6, 1, 4, 6, 1, 1, 2, 2, 3, 7, 1, 13, 6, 1, 4, 16, 5, 16, 1, 5, 31, 35, 3, 5, 2, 1, 2, 3, 1, 1, 2, 6, 1, 1, 12, 5, 1, 2
Offset: 1

Views

Author

Matthew Campbell, Sep 25 2015

Keywords

Comments

a(n) is also the smallest value of k at which b(k, n+1) - b(k, n) > 1.

Examples

			When n = 3, writing Composite(x) for A002808(x):
1. Composite(3) = 8. 8 + 1 = 9 = 3^2. 9 is not prime.
2. Composite(8) = 15. 15 + 1 = 16 = 2^4. 16 is not prime.
3. Composite(15) = 25. 25 + 1 = 26 = 2*13. 26 is not prime.
4. Composite(25) = 38. 38 + 1 = 39 = 3*13. 39 is not prime.
5. Composite(38) = 55. 55 + 1 = 56 = 2^3*7. 56 is not prime.
6. Composite(55) = 77. 77 + 1 = 78 = 2*3*13. 78 is not prime.
7. Composite(77) = 105. 105 + 1 = 106 = 2*53. 106 is not prime.
8. Composite(105) = 140. 140 + 1 = 141 = 3*47. 141 is not prime.
9. Composite(140) = 183. 183 + 1 = 184 = 2^3*23. 184 is not prime.
10. Composite(183) = 235. 235 + 1 = 236 = 2^2*59. 236 is not prime.
11. Composite(235) = 298. 298 + 1 = 299 = 13*23. 299 is not prime.
12. Composite(298) = 372. 372 + 1 = 373. 373 is prime.
--------------------------------------------------------------
Since the composite function was applied 12 times, a(3)=12.

Links

Crossrefs

Primes and nonprimes: A000040, A002808, A008578, A018252.
a(1) = p, a(n+1) = a(n)-th composite number: A006508, A022450, A022451, A025010, A025011, A059407, A059408.
Composites with order n > 1: A050435, A050436, A050438, A050439, A050440.
Composites with order n = b, n >= 1: A022449.
Composites with prime subscripts: A065858.
Composites without prime subscripts: A175251.
Order of compositeness: A059981, A236536.
Prime(n)-1: A006093.

Programs

  • Mathematica
    c = Select[Range[10^5], CompositeQ]; Table[k = 1; While[! PrimeQ[Nest[c[[#]] &, n, k] + 1], k++]; k, {n, 120}] (* Michael De Vlieger, Jul 15 2016 *)

Extensions

Terms from a(12) onward from Jon E. Schoenfield, Sep 27 2015
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.