1,1

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

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)

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 *)

(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

(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

Cf. A000040, A002144, A002145, A102261, A108547 (fixed points), A108548, A111745, A332806 (inverse), A332807, A332894 (left inverse).

Left edge of A332815, right edge of A332817, leftmost column of A389088.

Cf. also A111744, A267101, A332211, A339900, A348744.

Sequence in context: A387523 A067836 A332806 * A065107 A338944 A351528

Adjacent sequences: A108543 A108544 A108545 * A108547 A108548 A108549

Reinhard Zumkeller, Jun 10 2005

approved