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 1-3 of 3 results.

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

Views

Author

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

Keywords

Examples

			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.

Links

Crossrefs

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

Programs

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

Extensions

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

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

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 1-3 of 3 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.