A126273 a(0) = a(1) = a(2) = 1, a(n) = largest prime <= a(n-1) + a(n-2) + a(n-3).

1, 1, 1, 3, 5, 7, 13, 23, 43, 79, 139, 257, 467, 863, 1583, 2909, 5351, 9839, 18097, 33287, 61223, 112603, 207113, 380929, 700643, 1288657, 2370223, 4359517, 8018383, 14748119, 27126019, 49892519, 91766581, 168785119, 310444181

Offset: 0

Author

Jonathan Vos Post, Mar 09 2007

Keywords

• easy
• nonn

Comments

Analog of A055500 a(0)=1, a(1)=1, a(n) = largest prime <= a(n-1)+a(n-2). Might be called the Prime-tribonacci sequence. a(n) is asymptotic to c*T^n where T is the tribonacci constant 1.83928675 whose digits are A058265 for a real constant c.

Examples

			a(3) = 3 = a(0)+a(1)+a(2) = 1+1+1 = 3.
a(4) = 5 = a(1)+a(2)+a(3) = 1+1+3 = 5.
a(5) = 7 < a(2)+a(3)+a(4) = 1+3+5 = 9.
a(6) = 13 < a(3)+a(4)+a(5) = 3+5+7 = 15.
a(7) = 23 < a(4)+a(5)+a(6) = 5+7+13 = 25.
a(8) = 43 = a(5)+a(6)+a(7) = 7+13+23 = 43.
a(9) = 79 = a(6)+a(7)+a(8) = 13+23+43 = 79.
a(10) = 139 < a(7)+a(8)+a(9) = 23+43+79 = 145.
		

Crossrefs

Cf. A000040, A000073, A055500, A058265.

Programs

Maple

a[0]:=1:a[1]:=1:a[2]:=1:for n from 3 to 40 do a[n]:=prevprime(1+a[n-1]+a[n-2]+a[n-3]) od: seq(a[n],n=0..40); # Emeric Deutsch, Mar 24 2007

Extensions

More terms from Emeric Deutsch, Mar 24 2007

Offset corrected by N. J. A. Sloane, Jun 16 2021