cp's OEIS Frontend

A243914 Even numbers which are twice the sum of a twin prime pair, but cannot be expressed as the sum of 2 distinct twin prime pairs.

%I A243914 #24 Jun 16 2014 02:30:48
%S A243914 16,24,792,1392
%N A243914 Even numbers which are twice the sum of a twin prime pair, but cannot be expressed as the sum of 2 distinct twin prime pairs.
%C A243914 Subsequence of A111046 (twice A054735).
%C A243914 It seems that this sequence is probably finite (there are no further terms below 10^7).
%e A243914 a(1) = 16 = 2*(3+5).
%e A243914 16 is in the sequence since it is twice the sum of twin primes 3 and 5, but cannot be expressed as the sum of 2 distinct twin pairs.
%e A243914 36 is not in the sequence because although it is the sum of twin primes 17 and 19, it can also be expressed as the sum of pairs (5, 7) and (11, 13).
%p A243914 with(SignalProcessing): # requires at least Maple 17
%p A243914 N:= 10^6; # to check primes up to N
%p A243914 Primes:= select(isprime,{seq(2*i+1,i=1..N)}):
%p A243914 Twins:= Primes intersect map(t-> t-2,Primes):
%p A243914 nT:= nops(Twins);
%p A243914 T:= Array(1..(Twins[nT]+1)/2, datatype=float[8]);
%p A243914 for i from 1 to nT do T[(Twins[i]+1)/2]:= 1 od:
%p A243914 TTwins:= Convolution(T,T);
%p A243914 map(t -> 4*(t+1), select(n -> round(TTwins[n])=1,[$1..(nT+1)/2])); # _Robert Israel_, Jun 15 2014
%o A243914 (PARI) isok(isum1, vsum2) = {for (k=1, #vsum2, ksum2 = vsum2[k]; if (ksum2 > one, break;); if (isum1 - ksum2 != ksum2, if (vecsearch(vsum2, isum1 - ksum2), return (0)););); return (1);}
%o A243914 lista() = {v = readvec("b014574.txt"); vsum1 = 4*v; vsum2 = 2*v; maxs2 = vecmax(vsum2); for (i=1, #v, isum1 = vsum1[i]; if (isum1 < maxs2, if (isok(isum1, vsum2), print1(isum1, ", "));););} \\ _Michel Marcus_, Jun 15 2014
%o A243914 (PARI) l1=l2=List();a=select(p->isprime(p+2),primes(1000));for(i=1,#a-1,if(i<#a/4,listput(l1,4*a[i]+4));for(j=i+1,#a,listput(l2,2*(a[i]+a[j])+4)));print(setminus(Set(l1),Set(l2))) \\ _Lear Young_, Jun 15 2014
%Y A243914 Cf. A054735, A111046.
%K A243914 nonn
%O A243914 1,1
%A A243914 _Lear Young_, Jun 14 2014