A113057 - OEIS

%I #19 Jun 15 2024 02:19:39

%S 1,1,1,3,4,8,9,21,22,23,24,69,70,163,164,165,166,495,496,1157,1158,

%T 1159,1160,3477,3478,3479,3480,3481,3482,10443,10444,24369,24370,

%U 24371,24372,24373,24374,73119,73120,73121,73122,219363,219364,511849,511850,511851

%N a(1) = a(2) = a(3) = 1; for n>3, a(n) = a(n-1) + a(n-2) + a(n-3) iff n-1 is prime, otherwise a(n) = a(n-1) + 1.

%e a(4) = 3 because 4-1 = 3 is prime, so a(4) = a(3) + a(2) + a(1) = 1 + 1 + 1 = 3.

%e a(5) = 4 because 5-1 = 4 is not prime, so a(5) = a(4) + 1 = 3 + 1 = 4.

%e a(6) = 8 because 6-1 = 5 is prime, so a(6) = a(5) + a(4) + a(3) = 4 + 3 + 1 = 8.

%e a(7) = 9 because 7-1 = 6 is not prime, so a(7) = a(6) + 1 = 8 + 1 = 9.

%e a(8) = 21 because 8-1 = 7 is prime, so a(8) = a(7) + a(6) + a(5) = 9 + 8 + 4 = 21.

%t a[1]=a[2]=a[3]=1;a[n_]:=If[PrimeQ[n-1],a[n-1]+a[n-2]+a[n-3],a[n-1]+1];Table[a[n],{n,46}] (* _James C. McMahon_, Jun 14 2024 *)

%Y Cf. A000040, A000073, A000213, A001590, A113050, A113051, A113058.

%K easy,nonn

%O 1,4

%A _Jonathan Vos Post_, Oct 13 2005

%E Name edited and data corrected beginning at a(32) by _James C. McMahon_, Jun 14 2024