A352233 Numbers that can be expressed as the sum of two primes in exactly 10 ways.

114, 126, 162, 260, 290, 304, 316, 328, 344, 352, 358, 374, 382, 416, 542, 632

Offset

1,1

Comments

All terms are even. Conjecture: 632 is the last term. Hardy and Littlewood conjectured a grow rate of the number of decompositions for large even numbers (see Conjecture A in page 32 of Hardy and Littlewood reference), implying this sequence is finite. - Chai Wah Wu, Mar 10 2022

Links

Table of n, a(n) for n=1..16.

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).

Example

114 = 5+109 = 7+107 = 11+103 = 13+101 = 17+97 = 31+83 = 41+73 = 43+71 = 47+67 = 53+61.

Mathematica

c[n_] := Count[IntegerPartitions[n, {2}], _?(And @@ PrimeQ[#] &)]; Select[Range[1000], c[#] == 10 &] (* Amiram Eldar, Mar 08 2022 *)

Crossrefs

Numbers that can be expressed as the sum of two primes in k ways for k=0..10: A014092 (k=0), A067187 (k=1), A067188 (k=2), A067189 (k=3), A067190 (k=4), A067191 (k=5), A066722 (k=6), A352229 (k=7), A352230 (k=8), A352231 (k=9), this sequence (k=10).

Sequence in context: A228961 A057440 A113537 * A127664 A063991 A292020

Adjacent sequences: A352230 A352231 A352232 * A352234 A352235 A352236

Keyword

nonn,more

Author

Wesley Ivan Hurt, Mar 08 2022

Status

approved