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

0,1

Comments

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

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..10000

Index entries for sequences related to Goldbach conjecture

Example

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.

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]

Crossrefs

Cf. A071681, A126204.

Sequence in context: A102978 A218537 A236969 * A107165 A066811 A269414

Adjacent sequences: A222587 A222588 A222589 * A222591 A222592 A222593

Keyword

nonn

Author

Robert G. Wilson v, Feb 25 2013

Status

approved