A113057 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.

1, 1, 1, 3, 4, 8, 9, 21, 22, 23, 24, 69, 70, 163, 164, 165, 166, 495, 496, 1157, 1158, 1159, 1160, 3477, 3478, 3479, 3480, 3481, 3482, 10443, 10444, 24369, 24370, 24371, 24372, 24373, 24374, 73119, 73120, 73121, 73122, 219363, 219364, 511849, 511850, 511851

Offset

1,4

Links

Table of n, a(n) for n=1..46.

Example

a(4) = 3 because 4-1 = 3 is prime, so a(4) = a(3) + a(2) + a(1) = 1 + 1 + 1 = 3.
a(5) = 4 because 5-1 = 4 is not prime, so a(5) = a(4) + 1 = 3 + 1 = 4.
a(6) = 8 because 6-1 = 5 is prime, so a(6) = a(5) + a(4) + a(3) = 4 + 3 + 1 = 8.
a(7) = 9 because 7-1 = 6 is not prime, so a(7) = a(6) + 1 = 8 + 1 = 9.
a(8) = 21 because 8-1 = 7 is prime, so a(8) = a(7) + a(6) + a(5) = 9 + 8 + 4 = 21.

Mathematica

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 *)

Crossrefs

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

Sequence in context: A165362 A245282 A320355 * A253606 A258640 A345223

Adjacent sequences: A113054 A113055 A113056 * A113058 A113059 A113060

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 13 2005

Extensions

Name edited and data corrected beginning at a(32) by James C. McMahon, Jun 14 2024

Status

approved