A128609 a(1)=a(2)=1; a(n) = a(n-2) + a(n-1) + (number of terms from among {a(1), a(2), ..., a(n-1)} which are prime).

1, 1, 2, 4, 7, 13, 23, 40, 67, 112, 184, 301, 490, 796, 1291, 2093, 3390, 5489, 8885, 14380, 23271, 37657, 60935, 98599, 159541, 258148, 417697, 675853, 1093558, 1769419, 2862985, 4632412, 7495405, 12127825, 19623238, 31751071, 51374317

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

There are 5 prime among the first 9 terms of the sequence. So a(10) = a(8) + a(9) + 5 = 40 + 67 + 5 = 112.

Maple

a[1]:=1: a[2]:=1: for n from 3 to 45 do ct:=0: a[n]:=a[n-1]+a[n-2]+ct: for j from 3 to n-1 do if isprime(a[j])=true then a[n]:=a[n]+1 else fi od: od: seq(a[n], n=1..45); # Emeric Deutsch, May 25 2007

Mathematica

nxt[{a_, b_, p_}]:={b, a+b+p, If[PrimeQ[a+b+p], p+1, p]}; Transpose[ NestList[ nxt, {0, 1, 0}, 40]][[2]] (* Harvey P. Dale, May 01 2014 *)

Crossrefs

Sequence in context: A054150 A130709 A051013 * A335471 A168043 A114832

Adjacent sequences: A128606 A128607 A128608 * A128610 A128611 A128612

Keyword

nonn

Author

Leroy Quet, May 08 2007

Extensions

More terms from Emeric Deutsch, May 25 2007

Status

approved