%I #19 Mar 15 2015 09:09:34

%S 1,1,1,3,3,5,5,7,7,9,13,9,15,17,11,19,23,17,21,29,21,23,35,25,29,43,

%T 29,31,47,31,35,61,35,41,63,45,43,69,51,47,75,57,49,85,59,53,87,71,65,

%U 91,73,69,97,75,79,103,81,85,105,87,89,107,97,103,111,99,107,125,105,117

%N Sums of three successive terms form the odd primes.

%H Reinhard Zumkeller, <a href="/A073737/b073737.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) + a(n-1) + a(n-2) = n-th prime, where a(0)=1, a(-1)=0, a(-2)=0 and the 0th prime is taken to be 1.

%e At n=10, a(10) + a(9) + a(8) = 13 + 9 + 7 = 29 = p_10.

%t a[0] = 1; a[-1] = 0; a[-2] = 0; p[0] = 1; p[n_?Positive] := Prime[n]; a[n_] := a[n] = p[n] - a[n-1] - a[n-2]; Table[a[n], {n, 0, 69}] (* _Jean-François Alcover_, Sep 30 2011 *)

%t nxt[{a_,b_,c_}]:={b,c,NextPrime[a+b+c]-(b+c)}; Transpose[NestList[nxt,{1,1,1},70]][[1]] (* _Harvey P. Dale_, Mar 15 2015 *)

%o (Haskell)

%o a073737 n = a073737_list !! (n-1)

%o a073737_list =

%o 1 : 1 : zipWith (-) a065091_list

%o (zipWith (+) a073737_list $ tail a073737_list)

%o -- _Reinhard Zumkeller_, Aug 14 2011

%Y Cf. A036467, A001223, A073736.

%Y Cf. A065091, A000040.

%K easy,nice,nonn

%O 1,4

%A _Paul D. Hanna_, Aug 07 2002