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.

16, 24, 792, 1392

Offset

1,1

Comments

Subsequence of A111046 (twice A054735).

It seems that this sequence is probably finite (there are no further terms below 10^7).

Links

Table of n, a(n) for n=1..4.

Example

a(1) = 16 = 2*(3+5).
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.
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).

Maple

with(SignalProcessing): # requires at least Maple 17
N:= 10^6; # to check primes up to N
Primes:= select(isprime, {seq(2*i+1, i=1..N)}):
Twins:= Primes intersect map(t-> t-2, Primes):
nT:= nops(Twins);
T:= Array(1..(Twins[nT]+1)/2, datatype=float[8]);
for i from 1 to nT do T[(Twins[i]+1)/2]:= 1 od:
TTwins:= Convolution(T, T);
map(t -> 4*(t+1), select(n -> round(TTwins[n])=1, [$1..(nT+1)/2])); # Robert Israel, Jun 15 2014

Prog

(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); }
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
(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

Crossrefs

Cf. A054735, A111046.

Sequence in context: A166629 A066261 A256526 * A226296 A070571 A087622

Adjacent sequences: A243911 A243912 A243913 * A243915 A243916 A243917

Keyword

nonn

Author

Lear Young, Jun 14 2014

Status

approved