A073737 Sums of three successive terms form the odd primes.

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, 29, 31, 47, 31, 35, 61, 35, 41, 63, 45, 43, 69, 51, 47, 75, 57, 49, 85, 59, 53, 87, 71, 65, 91, 73, 69, 97, 75, 79, 103, 81, 85, 105, 87, 89, 107, 97, 103, 111, 99, 107, 125, 105, 117

Offset: 1

Author

Paul D. Hanna, Aug 07 2002

Keywords

• easy
• nice
• nonn

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A036467, A001223, A073736.

Cf. A065091, A000040.

Programs

Haskell

a073737 n = a073737_list !! (n-1)
a073737_list =
   1 : 1 : zipWith (-) a065091_list
                       (zipWith (+) a073737_list $ tail a073737_list)
-- Reinhard Zumkeller, Aug 14 2011

Mathematica

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 *)
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 *)

Formula

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.