

A139324


Difference between two sequences of primes which indicate two different kinds of places in the prime sequence with some vanishing thirdorder difference.


1



4, 4, 4, 4, 6, 4, 6, 4, 4, 6, 6, 6, 8, 6, 4, 4, 6, 8, 8, 6, 6, 4, 4, 4, 4, 6, 4, 6, 4, 6, 4, 8, 6, 4, 4, 6, 4, 10, 4, 6, 4, 6, 18, 12, 4, 4, 6, 6, 4, 6, 6, 8, 10, 12, 8, 6, 4, 6, 6, 8, 4, 12, 4, 4, 6, 6, 8, 4, 4, 4, 4, 6, 12
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OFFSET

1,1


COMMENTS

There are two sequences of primes at which two thirdorder differences vanish:
one is b(n) = 23, 41, 47, 71, 89, 233, ... which contains all primes prime(n) such that prime(n2)  3*prime(n1) + 3*prime(n)  prime(n+1) = 0;
the other is A139313(n) = 19, 37, 43, ... such that prime(n1) + 3*prime(n)  3*prime(n+1)  prime(n+2) = 0.
Then by definition a(n) = b(n)  A139313(n).


LINKS



EXAMPLE

23  19 = 4 = a(1). 41  37 = 4 = a(2). 47  43 = 4 = a(3).


MAPLE

A139324a := proc(n) if n = 1 then 23; else a := nextprime(procname(n1)) ; while (true ) do if prevprime(prevprime(a))3*prevprime(a)+3*anextprime(a) =0 then return a; end if; a := nextprime(a) ; end do: end if; end proc:
A139313 := proc(n) if n = 1 then 19; else a := nextprime(procname(n1)) ; while (true ) do if prevprime(a)+3*a3*nextprime(a)+nextprime(nextprime(a)) = 0 then return a; end if; a := nextprime(a) ; end do: end if; end proc:


MATHEMATICA

Flatten[Table[If[ Prime[ 2 +n]  3 Prime[ 1 + n] + 3 Prime[n]  1 Prime[1 + n] == 0, Prime[n], {}], {n, 3, 500}]]  Flatten[ Table[If[ Prime[ 1 + n] + 3*Prime[n]  3*Prime[1 + n] + Prime[n + 2] == 0, Prime[n], {}], {n, 2, 500}]]


CROSSREFS



KEYWORD

nonn,less


AUTHOR



STATUS

approved



