A120761 - OEIS

%I #16 Oct 09 2024 11:06:40

%S 1,1,2,3,5,8,13,18,31,44,75,106,137,168,305,442,579,716,853,990,1843,

%T 2696,3549,4402,5255,6108,6961,7814,14775,21736,28697,35658,64355,

%U 93052,121749,150446,179143,207840,386983,566126,745269,924412,1103555

%N a(1) = a(2) = 1. a(n) = a(n-1) + (largest noncomposite {1 or prime} among the first n-2 terms of the sequence).

%H Michael De Vlieger, <a href="/A120761/b120761.txt">Table of n, a(n) for n = 1..10000</a>

%e Among the first 10 terms of the sequence, 31 is the largest noncomposite. So a(12) = a(11) + 31 = 75 + 31 = 106.

%p isA008578 := proc(n) if n = 1 or isprime(n) then true ; else false ; fi ; end: A120761 := proc(nmin) local a,lnpr,k; a := [1,1,2] ; while nops(a) < nmin do lnpr :=0 ; for k in [op(1..nops(a)-1,a)] do if isA008578(k) then lnpr := max(lnpr,k) ; fi ; od: a := [op(a),a[ -1]+lnpr] ; od: RETURN(a) ; end: A120761(80) ; # _R. J. Mathar_, Sep 18 2007

%t s={1,1};Do[AppendTo[s,s[[-1]]+Max[Select[Drop[s,-1],!CompositeQ[#]&]]],{n,3,43}];s (* _James C. McMahon_, Oct 09 2024 *)

%Y Cf. A120760.

%K nonn

%O 1,3

%A _Leroy Quet_, Jul 03 2006

%E More terms from _R. J. Mathar_, Sep 18 2007