A108546 Lexicographically earliest permutation of primes such that for n>1 forms 4*k+1 and 4*k+3 alternate.

2, 3, 5, 7, 13, 11, 17, 19, 29, 23, 37, 31, 41, 43, 53, 47, 61, 59, 73, 67, 89, 71, 97, 79, 101, 83, 109, 103, 113, 107, 137, 127, 149, 131, 157, 139, 173, 151, 181, 163, 193, 167, 197, 179, 229, 191, 233, 199, 241, 211, 257, 223, 269, 227, 277, 239, 281, 251, 293

Offset: 1

Author

Reinhard Zumkeller, Jun 10 2005

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A002144, A002145, A102261, A108547 (fixed points), A108548, A111745, A332806 (inverse), A332807.

Cf. also A267101, A332211.

Programs

Haskell

import Data.List (transpose)
a108546 n = a108546_list !! (n-1)
a108546_list =  2 : concat
   (transpose [a002145_list, a002144_list])
-- Reinhard Zumkeller, Nov 13 2014, Feb 22 2011

Mathematica

terms = 60; A111745 = Module[{prs = Prime[Range[2terms]], m3, m1, min}, m3 = Select[prs, Mod[#, 4] == 3&]; m1 = Select[prs, Mod[#, 4] == 1&]; min = Min[Length[m1], Length[m3]]; Riffle[Take[m3, min], Take[m1, min]]]; a[1] = 2; a[n_] := A111745[[n-1]]; Table[a[n], {n, 1, terms}] (* Jean-François Alcover, May 18 2017, using Harvey P. Dale's code for A111745 *)

PARI

up_to = 10000;
A108546list(up_to) = { my(v=vector(up_to), p,q); v[1] = 2; v[2] = 3; v[3] = 5; for(n=4,up_to, p = v[n-2]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[n] = q); (v); };
v108546 = A108546list(up_to);
A108546(n) = v108546[n]; \\ Antti Karttunen, Feb 27 2020

Formula

a(n) mod 4 = 3 - 2 * (n mod 2) for n>1.

For n > 1: a(n) = A111745(n-1).

a(2*n+1) - a(2*n) = A102261(n).

From Antti Karttunen, Feb 27 2020: (Start)

a(1) = 2, a(2n) = A002145(n), a(2n+1) = A002144(n).

a(n) = A000040(A332807(n)).

(End)