A352298 Conjectured largest number that can be expressed as the sum of two primes in exactly n ways or -1 if no such number exists.

-1, -1, 68, 128, 152, 188, 332, 398, 368, 488, 632, 692, 626, 992, 878, 908, 1112, 998, 1412, 1202, 1448, 1718, 1532, 1604, 1682, 2048, 2252, 2078, 2672, 2642, 2456, 2936, 2504, 2588, 2978, 3092, 3032, 3218, 3272, 3296, 3632, 3548, 3754, 4022, 4058, 4412, 4448

Offset: 0

Author

Chai Wah Wu, Mar 11 2022

Keywords

• sign

Comments

Conjecture A in page 32 of the Hardy and Littlewood reference implies that a(n) != -1 for all n > 1. While the sequence is not monotonic, the plot of n versus a(n)/log(a(n))^2 has a linear trend which matches with the formula for the number of representations in Conjecture A.

Links

• G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes, Acta Mathematica, volume 44, pages 1-70 (1923).

Crossrefs

Cf. A352296.

Essentially the same as A000954.