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.

A064916 a(n) = n/lpf(n) + lpf(n) - 1, where lpf = A020639 = least prime factor.

Original entry on oeis.org

2, 3, 3, 5, 4, 7, 5, 5, 6, 11, 7, 13, 8, 7, 9, 17, 10, 19, 11, 9, 12, 23, 13, 9, 14, 11, 15, 29, 16, 31, 17, 13, 18, 11, 19, 37, 20, 15, 21, 41, 22, 43, 23, 17, 24, 47, 25, 13, 26, 19, 27, 53, 28, 15, 29, 21, 30, 59, 31, 61, 32, 23, 33, 17, 34, 67, 35, 25, 36, 71, 37, 73, 38, 27
Offset: 2

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Author

Reinhard Zumkeller, Oct 14 2001

Keywords

Comments

a(n) = A032742(n) + A020639(n) - 1; a(n) <= n and for n > 1 a(n) = n iff n is prime.

Examples

			a(18) = 18/2 + 2 - 1 = 10;
a(19) = 19/19 + 19 - 1 = 19.

Links

Crossrefs

Cf. A064920, A064917, A064918, A032742, A020639, A064919.

Programs

  • Mathematica
    lpf[n_]:=Module[{lp=FactorInteger[n][[1,1]]},n/lp+lp-1]; Array[lpf, 80, 2] (* Harvey P. Dale, Sep 25 2011 *)
  • PARI
    lpf(n)= { local(f); f=factor(n); return(f[1, 1]) } { for (n=2, 1000, L=lpf(n); a=n / L + L - 1; write("b064916.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 28 2009
  • PARI
    a(n) = my(p = vecmin(factor(n)[,1])); n/p + p - 1; \\ Michel Marcus, Jun 19 2018

A064918 a(n) is the number of iterations of k -> A064916(k) to reach a prime, starting at n.

Original entry on oeis.org

0, 0, 1, 0, 2, 0, 1, 1, 3, 0, 1, 0, 2, 1, 2, 0, 4, 0, 1, 2, 2, 0, 1, 2, 3, 1, 2, 0, 3, 0, 1, 1, 5, 1, 1, 0, 2, 2, 3, 0, 3, 0, 1, 1, 2, 0, 3, 1, 4, 1, 2, 0, 3, 2, 1, 3, 4, 0, 1, 0, 2, 1, 2, 1, 6, 0, 2, 3, 2, 0, 1, 0, 3, 2, 3, 1, 4, 0, 1, 1, 4, 0, 1, 3, 2, 1, 2, 0, 3, 1, 1, 2, 4, 1, 2, 0, 5, 2, 2, 0, 3, 0, 1, 1, 4
Offset: 2

Views

Author

Reinhard Zumkeller, Oct 14 2001

Keywords

Comments

a(p) = 0 for all primes p.

Examples

			a(6) = 2 as A064916(A064916(6)) = A064916(4) = 3 = A064917(6).

Links

Crossrefs

Cf. A064916, A064917, A064922.

Programs

  • PARI
    lpf(n)= { local(f); f=factor(n); return(f[1, 1]) } { for (n=2, 1000, m=n; a=0; while (!isprime(m), L=lpf(m); m=m / L + L - 1; a++); write("b064918.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 29 2009

A064921 Iterate A064920 until a prime is reached.

Original entry on oeis.org

2, 3, 3, 5, 3, 7, 5, 5, 3, 11, 3, 13, 5, 7, 5, 17, 5, 19, 5, 5, 3, 23, 3, 5, 5, 11, 3, 29, 3, 31, 17, 13, 5, 11, 5, 37, 5, 7, 3, 41, 3, 43, 5, 13, 3, 47, 5, 13, 5, 19, 5, 53, 5, 7, 5, 5, 3, 59, 5, 61, 17, 7, 13, 17, 5, 67, 5, 5, 5, 71, 5, 73, 5, 19, 3, 17, 5, 79, 5, 29, 3, 83, 5, 5, 5, 31, 5
Offset: 2

Views

Author

Reinhard Zumkeller, Oct 14 2001

Keywords

Comments

Well defined since A064920(n) < n for nonprimes.
a(p) = p for all primes p.

Examples

			a(18) = 5 as A064920(18) = 8 and A064920(8) = 5.

Links

Crossrefs

Cf. A064920, A064922, A064917.

Programs

  • PARI
    gpf(n)= { local(f); f=factor(n)~; return(f[1, length(f)]) } { for (n=2, 1000, m=n; while (!isprime(m), g=gpf(m); m=m / g + g - 1); write("b064921.txt", n, " ", m) ) } \\ Harry J. Smith, Sep 29 2009
Showing 1-3 of 3 results.

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