A011974 : Is 2 the sum of 2 successive primes?

[Alexander Povolotsky]

The exact definition of A011974 as shown in OEIS is:
"2 followed by the numbers that are the sum of 2 successive primes".
So the above definition never implies (but rather on opposite )
that 2 is the sum of 2 successive primes.

Before trying to "fix" it I suggest that Neil, who authored this
sequence, explain why this sequence starts with 2 (which is NOT the
sum of two successive primes) - perhaps there is a special reason for
this initial term to be there - I guess otherwise Neil would not keep
it as a separate sequence apart from A001043 ?

AP

On Feb 18, 2008 8:53 AM, zak seidov <zakseidov at yahoo.com> wrote:
> Thanks to all responding
> for idea about zeroth prime!
>
> I've found TWO cases in OEIS,
> both give p(0)=1, p(1)=2, and if so
> the initial term of A011974'd be 3 not 2,
> right?
> zak
>
> Search: "zeroth prime"
> Displaying 1-2 of 2 results found.
> %N A059871 Number of solutions to the equation p_i =
> (1+mod(i,2))*p_{i-1} +- p_{i-2} +- p_{i-3}
>                +- ... +- 2 +- 1, where p_i is the i-th
> prime number (where p_1 =
> 2, and the "zeroth prime" p_0 is here 1).
>
> %C A062241 Here we are taking 1 to be the zeroth
> prime.
>
>
> --- zak seidov <zakseidov at yahoo.com> wrote:
>
> >
> > A011974: Is 2 the sum of 2 successive primes?
> > zak
> >
> > %I A011974
> > %S A011974
> > 2,5,8,12,18,24,30,36,42,52,60,68,78,84,90,100,112
> > %N A011974 Numbers that are the sum of 2 successive
> > primes.
> > %D A011974 Archimedeans Problems Drive, Eureka, 26
> > (1963), 12.
> > %F A011974 Essentially same as A001043.
> >
> > %I A001043 M3780 N0968
> > %S A001043
> > 5,8,12,18,24,30,36,42,52,60,68,78,84,90,100,112
> > %N A001043 Numbers that are the sum of 2 successive
> > primes.
> > %D A001043 Archimedeans Problems Drive, Eureka, 26
> > (1963), 12.




Before trying to "fix" it I suggest that Neil, who authored this
this initial term to be there - I guess otherwise Neil would not keep
it as a separate sequence apart from A001043 ?


it came from



Just to wrap up this thread - I'm adding A137815 and A137816
and I'm updating A067704

Thanks to everyone who helped!

Neil