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First sums of successive twin primes of order n.
0

%I #4 Oct 01 2013 17:58:01

%S 8,18,40,92,216,508,1184,2730,6244,14210,32232,72886,164228,368508,

%T 823168,1830254,4050492,8922736,19567376,42726960,92925664,201364874,

%U 434900208,936411160,2010419024,4304117640,9189045664,19563691880

%N First sums of successive twin primes of order n.

%C Order here refers to the depth of the iterations in successive sums. Order 0 is the twin primes, order 1 is the sums of order 0, order 2 is the sums of order 1 etc.

%e The twin prime quartet 3,5,5,7 has the first order sums 8,10,12 and the 2nd order sums 18,22 and the 3rd order sums 40. The first of these are 8,18,40 the first 3 terms in the sequence.

%o (PARI) sucsumstwfirst(n,m) = { local(a,b,i,j,k,p); a = vector(1001); b = vector(1001); p=1; forprime(j=3,n, if(isprime(j+2), a[p] = j; a[p+1] = j+2; p+=2; ) ); for(i=1,m, for(j=1,n+n, b[j] = a[j]+ a[j+1]; ); a=b; print1(a[1]","); ) }

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Jun 23 2004