A120760 a(1) = a(2) = 1. a(n) = a(n-1) + (largest nonprime {1 or composite} among the first n-2 terms of the sequence).

1, 1, 2, 3, 4, 5, 9, 13, 22, 31, 53, 75, 97, 172, 247, 419, 666, 913, 1579, 2492, 3405, 5897, 9302, 12707, 22009, 34716, 56725, 91441, 148166, 239607, 387773, 627380, 1015153, 1642533, 2657686, 4300219, 6957905, 11258124, 18216029, 29474153

Offset

1,3

Links

Michael De Vlieger, Table of n, a(n) for n = 1..4792

Example

Among the first 8 terms of the sequence, 9 is the largest nonprime. So a(10) = a(9) + 9 = 22 + 9 = 31.

Maple

isA018252 := proc(n) if n = 1 or not isprime(n) then true ; else false ; fi ; end: A120760 := 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 isA018252(k) then lnpr := max(lnpr, k) ; fi ; od: a := [op(a), a[ -1]+lnpr] ; od: RETURN(a) ; end: A120760(80) ; # R. J. Mathar, Sep 18 2007

Mathematica

s={1, 1}; Do[AppendTo[s, s[[-1]]+Max[Select[Drop[s, -1], !PrimeQ[#]&]]], {n, 3, 40}]; s (* James C. McMahon, Oct 09 2024 *)

Prog

(PARI)
N=40; v=vector(N); v[1]=1; v[2]=1; for(n=3, N, v[n]=v[n-1]+vecmax(select(x->x==1||!isprime(x), v[1..n-2]))); v \\ Bruce Nye, Jan 16 2026

Crossrefs

Cf. A120761, A001622.

Sequence in context: A253181 A107365 A026484 * A245449 A337647 A346600

Adjacent sequences: A120757 A120758 A120759 * A120761 A120762 A120763

Keyword

nonn

Author

Leroy Quet, Jul 03 2006

Extensions

More terms from R. J. Mathar, Sep 18 2007

Status

approved