

A157478


a(n) is the least prime p such that p is greater than any previous term and is representable as the arithmetic mean of two other primes in exactly n different ways.


0



5, 11, 17, 37, 53, 89, 107, 127, 179, 197, 223, 233, 257, 263, 401, 409, 421, 449, 457, 661
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OFFSET

1,1


COMMENTS

A number p is representable as the arithmetic mean of two other primes in n ways if there are n values of k such that p + k and p  k are both prime.
If the restriction that a(n) must be greater than previous terms is removed then the sequence would be A126204.  Andrew Howroyd, Jan 12 2020


LINKS



EXAMPLE

a(1) = 5 because 5+2 are primes.
a(2) = 11 because 11+6, 11+8 are primes.
a(3) = 17 because 17+6, 17+12, 17+=14 are primes.
a(4) = 37 because 37+6, 37+24, 37+30, 37+34 are primes.
a(5) = 53 because 53+6, 53+30, 53+36, 53+48, 53+50 are primes.


MATHEMATICA

q=1; lst={}; Do[p=Prime[n]; i=0; Do[If[PrimeQ[pk]&&PrimeQ[p+k], i++; ], {k, 2, p, 2}]; If[i==q, AppendTo[lst, p]; q++ ], {n, 2*5!}]; lst


PROG

(PARI) a(n, lim=oo)={my(v=vector(n), r=1); forprime(p=5, lim, my(k=0); forprime(q=3, p2, k+=isprime(2*pq)); if(k==r, if(r==n, return(p)); r++))} \\ Andrew Howroyd, Jan 12 2020


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



