A222590 Greatest prime representable as the arithmetic mean of two other primes in n different ways, or 0 if no such prime exists.

3, 19, 31, 61, 79, 83, 199, 181, 229, 271, 277, 313, 293, 439, 389, 401, 499, 619, 601, 709, 859, 643, 787, 811, 743, 823, 1039, 1009, 1321, 1021, 1279, 1213, 1249, 1489, 1483, 1301, 1609, 1621, 1459, 1753, 1559, 1877, 2011, 2029, 1741, 1901, 2087, 2239, 2207

Offset: 0

Author

Robert G. Wilson v, Feb 25 2013

Keywords

• nonn

Comments

a(6681) is probably the only such term which equals zero.

Examples

			There are only two primes which are not the arithmetic mean of two other primes and they are 2 and 3. Therefore a(0)=3.
There are only three primes which are the arithmetic mean of two other primes in just one way. They are 5 = (3+7)/2, 7 = (3+11)/2, and 19 = (7+31)/2. Therefore a(1)=19.
There are only three primes which are the arithmetic mean of two other primes in just two ways. They are 11 = (3+19)/2 = (5+17)/2, 13 = (3+23)/2 = (7+19)/2, and 31 = (3+59)/2 = (19+43)/2. Therefore a(2)=31, etc.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A071681, A126204.

Programs

Mathematica

f[n_] := Block[{c = 0, k = 2, p = Prime@ n}, While[k + 1 < p, If[PrimeQ[p - k] && PrimeQ[p + k], c++ ]; k += 2]; c]; t = Table[0, {1000}]; Do[a = f@ n; If[a < 1001, t[[a + 1]] = Prime@ n; Print[{a, Prime@ n}]], {n, 5000}]; Take[t, 50]