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A126273
a(0) = a(1) = a(2) = 1, a(n) = largest prime <= a(n-1) + a(n-2) + a(n-3).
0
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
0,4
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.
EXAMPLE
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.
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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 09 2007
EXTENSIONS
More terms from Emeric Deutsch, Mar 24 2007
Offset corrected by N. J. A. Sloane, Jun 16 2021
STATUS
approved