A164912 Dual EKG: a(n) = A008619(A064413(n) - 1).

1, 1, 2, 3, 2, 5, 6, 4, 5, 3, 8, 9, 7, 4, 11, 12, 8, 10, 11, 6, 17, 14, 15, 13, 18, 14, 13, 7, 20, 18, 16, 17, 9, 26, 21, 19, 10, 29, 23, 20, 22, 23, 12, 35, 24, 25, 26, 27, 28, 25, 32, 30, 28, 33, 35, 29, 15, 44, 33, 31, 16, 47, 36, 32, 34, 37, 19, 56

Offset

1,3

Comments

First occurrences of n have ranks: 1, 3, 4, 8, 6, 7, 13, 11, 12, 18, ...

Second occurrences of n have ranks: 2, 5, 10, 14, 9, 20, ...

Triples of the form (a, b, a+b): (1,1,2), (3,2,5), (5,3,8), (7,4,11), (11,6,17), ... give sequence 2, 5, 8, 11, 17, ....

Every positive integer appears exactly twice. - Charlie Neder, Jan 12 2019

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = A008619(A064413(n)-1) = ceiling(A064413(n)/2). - Charlie Neder, Jan 12 2019

Mathematica

ekg[n_] := ekg[n] = Module[{ee, k},
     If[n <= 2, n, ee = Array[ekg, n - 1];
     For[k = 1, True, k++, If[FreeQ[ee, k] &&
     GCD[ekg[n - 1], k] != 1, Return[k]]]]];
a[n_] := Quotient[ekg[n] - 1, 2] + 1;
Array[a, 68] (* Jean-François Alcover, Nov 21 2021 *)

Crossrefs

Cf. A000027, A008619, A064413.

Sequence in context: A070673 A070669 A218613 * A289386 A088861 A088631

Adjacent sequences: A164909 A164910 A164911 * A164913 A164914 A164915

Keyword

nonn

Author

Paul Curtz, Aug 31 2009

Extensions

More terms from Charlie Neder, Jan 12 2019

Name modified by Jean-François Alcover, Nov 23 2021

Status

approved