

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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
The next term if it exists > 10^6.  Andrew Howroyd, Jan 12 2020


LINKS

Table of n, a(n) for n=1..20.


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

Cf. A126204.
Sequence in context: A030468 A277290 A085634 * A297583 A356756 A088903
Adjacent sequences: A157475 A157476 A157477 * A157479 A157480 A157481


KEYWORD

nonn,more


AUTHOR

Vladimir Joseph Stephan Orlovsky, Mar 01 2009


EXTENSIONS

Definition clarified by Andrew Howroyd, Jan 12 2020


STATUS

approved



