A102696 Number of positive even integers that can be written as the sum of 2 of the first n odd primes (not necessarily distinct).

1, 3, 5, 8, 11, 14, 17, 20, 23, 28, 32, 37, 40, 44, 47, 50, 57, 61, 66, 70, 73, 78, 83, 89, 94, 99, 103, 107, 110, 117, 122, 127, 134, 139, 144, 150, 154, 160, 165, 170, 177, 181, 187, 192, 196, 202, 207, 215, 220, 227, 231, 236, 242, 247, 250, 253, 261, 269, 274, 278

Offset: 1

Author

Gabriel Cunningham (gcasey(AT)mit.edu), Feb 04 2005

Keywords

• easy
• nonn

Comments

A105047(n+2) = a(n+1) - a(n). - Reinhard Zumkeller, Aug 11 2015

Examples

			a(3) = 5 because with the primes {3, 5, 7} one can write 6 = 3+3, 8 = 3+5, 10 = 5+5, 12 = 5+7 and 14 = 7+7, for a total of 5 even numbers.
a(3) = 5 because with the primes {3, 5, 7} one can write 6 = 3+3, 8 = 3+5, 10 = 5+5 & 3+7, 12 = 5+7 and 14 = 7+7, for a total of 5 even numbers.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A105047 (first differences).

Programs

Haskell

import Data.List (nub)
a102696 n = length $ nub
   [p + q | p <- take n a065091_list, q <- takeWhile (<= p) a065091_list]
-- Reinhard Zumkeller, Aug 11 2015

Maple

N:= 1000: # to get first N terms
Primes:= {seq(ithprime(i),i=2..N+1)}:
S:= {}:
for n from 1 to N do
S:= S union map(`+`,Primes[1..n],Primes[n]);
A[n]:= nops(S);
od:
seq(A[n],n=1..N); # Robert Israel, Sep 03 2014

Mathematica

f[n_] := Block[{tp = Table[ Prime[i], {i, 2, n + 1}]}, Length[ Union[ Flatten[ Table[tp[[i]] + tp[[j]], {i, n}, {j, i}]] ]]]; Table[ f[n], {n, 60}] (* Robert G. Wilson v, Feb 05 2005 *)

PARI

a(n)=my(P=prime(n+1),s); forstep(k=6,2*P,2, forprime(p=max(k-P,3), min(P,k/2), if(isprime(k-p), s++; break))); s \\ Charles R Greathouse IV, Sep 04 2014

PARI

list(n)=my(P=prime(n+1),u=vectorsmall(P),v=vector(n),k); forprime(p=3,P, forprime(q=3,p,u[(p+q)/2]=1); v[k++]=sum(i=1,p,u[i])); v \\ Charles R Greathouse IV, Sep 04 2014

Extensions

More terms from Robert G. Wilson v, Feb 05 2005