OFFSET
1,1
COMMENTS
Conjecture: except for the 2nd, 3rd and 4th terms, all other terms are divisible by 3; See also comments in A103151.
a(23)=725 is also not divisible by 3. [D. S. McNeil, Sep 06 2010]
The only terms a(n) not divisible by 3 for n <= 1450 are a(2),a(3),a(4) and a(23). - Robert Israel, Mar 17 2020
LINKS
Robert Israel, Table of n, a(n) for n = 1..1450
EXAMPLE
9 is the smallest odd number with just one such composition: 9 = 3+2*3, thus a(1)=9.
Similarly, 13 is smallest with exactly 2 compositions: 13 = 3+2*5 = 7+2*3, thus a(2)=13.
MAPLE
N:= 2000: # for terms before the first term > N
P:= select(isprime, [seq(i, i=3..N, 2)]):
nP:= nops(P):
V:= Vector(N):
for i from 1 while 2*P[i]<N do
for j from 1 to nP do
k:= 2*P[i]+P[j];
if k > N then break fi;
V[k]:= V[k]+1;
od od:
A:= Vector(N):
for i from 1 to N by 2 do if V[i] <> 0 and A[V[i]] = 0 then A[V[i]]:= i fi od:
for i from 1 to N do if A[i] = 0 then break fi od:
seq(A[j], j=1..i-1); # Robert Israel, Mar 17 2020
MATHEMATICA
Array[a, 300]; Do[a[n] = 0, {n, 1, 300}]; n = 9; ct = 0; While[ct < 200, m = 3; ct = 0; While[(m*2) < n, If[PrimeQ[m], cp = n - (2* m); If[PrimeQ[cp], ct = ct + 1]]; m = m + 2]; If[a[ct] == 0, a[ct] = n]; n = n + 2]; Print[a]
PROG
(define (first-n-where-fun_n-is-i1 fun i) (let loop ((n 1)) (cond ((= i (fun n)) n) (else (loop (+ n 1)))))) ;; Antti Karttunen, Jun 19 2007
CROSSREFS
KEYWORD
nonn
AUTHOR
Lei Zhou, Feb 09 2005
EXTENSIONS
Starting offset changed from 0 to 1 by Antti Karttunen, Jun 19 2007
STATUS
approved