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.

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A072010 In prime factorization of n replace all primes of form k*4+1 with k*4+3 and primes of form k*4+3 with k*4+1.

Original entry on oeis.org

1, 2, 1, 4, 7, 2, 5, 8, 1, 14, 9, 4, 15, 10, 7, 16, 19, 2, 17, 28, 5, 18, 21, 8, 49, 30, 1, 20, 31, 14, 29, 32, 9, 38, 35, 4, 39, 34, 15, 56, 43, 10, 41, 36, 7, 42, 45, 16, 25, 98, 19, 60, 55, 2, 63, 40, 17, 62, 57, 28, 63, 58, 5, 64, 105, 18, 65, 76, 21, 70, 69
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 05 2002

Keywords

Comments

a(3^n) = 1; a(2^n) = 2^n;
a(n)>2 is prime iff n=m*3^i (i>=0), a(n)=a(m) and (m,a(m)) or (a(m),m) is a twin prime pair of form ((4*k+1),(4*k+3)), a(m)*m=A071697(j)=A071695(j)*A071696(j) for some j.

Examples

			a(26928) = a(2^4*3^2*11*17) = a(2)^4 * a(3)^2 * a(11) * a(17)
= 2^4 * 1^2 * 9 * 19 = 2736.

Links

Crossrefs

Cf. A002144, A002145, A072012(n) = a(a(n)).
For a(n) = n see A072011.
Cf. A072014, A072015.
Cf. A027746.

Programs

  • Haskell
    a072010 1 = 1
a072010 n = product $ map f $ a027746_row n where
   f 2 = 2
   f p = p + 2 * (2 - p `mod` 4)
-- Reinhard Zumkeller, Apr 09 2012
  • Mathematica
    a[1] = 1; a[p_?PrimeQ] = p + 2*(2 - Mod[p, 4]); a[n_] := Times @@ (a[#[[1]]]^#[[2]] & ) /@ FactorInteger[n]; Table[a[n], {n, 1, 71}] (* Jean-François Alcover, May 04 2012 *)

Formula

Multiplicative with a(p) = p + 2*(2 - p mod 4), p prime.

A072015 Maxima when the mapping of A072010 is applied to n repeatedly.

Original entry on oeis.org

1, 2, 1, 4, 7, 2, 7, 8, 1, 14, 9, 4, 15, 14, 7, 16, 19, 2, 19, 28, 7, 18, 21, 8, 49, 30, 1, 28, 31, 14, 31, 32, 9, 38, 35, 4, 39, 38, 15, 56, 43, 14, 43, 36, 7, 42, 45, 16, 49, 98, 19, 60, 63, 2, 63, 56, 19, 62, 57, 28, 63, 62, 7, 64, 105, 18, 105, 76, 21, 70
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 05 2002

Keywords

Examples

			The trajectory of 89 under the A072010-mapping is:
89 ->91 ->75 ->49 ->25 ->49 ..., therefore a(89) = 91.

Crossrefs

Cf. A072014.
Showing 1-2 of 2 results.

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

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