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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[p-k]&&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, p-2, k+=isprime(2*p-q)); 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

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Last modified December 5 02:23 EST 2022. Contains 358572 sequences. (Running on oeis4.)