A373664 Positive integers that cannot be written as a sum of a practical number and a 12-gonal number.

10, 11, 15, 22, 23, 26, 27, 38, 46, 47, 50, 58, 59, 62, 71, 74, 77, 83, 86, 95, 98, 103, 110, 114, 115, 119, 122, 131, 134, 139, 143, 146, 149, 155, 166, 167, 170, 175, 178, 179, 182, 187, 191, 194, 202, 203, 206, 207, 215, 227, 230, 238, 239, 242, 248, 250

Offset: 1

Author

Duc Van Khanh Tran, Jun 12 2024

Keywords

• nonn

Comments

Somu and Tran (2024) proved that there are infinitely many such integers. More generally, infinitely many positive integers cannot be written as a sum of a practical number and an s-gonal number if s is a multiple of 12.

Links

• Duc Van Khanh Tran, Table of n, a(n) for n = 1..10000
• Sai Teja Somu and Duc Van Khanh Tran, On sums of practical numbers and polygonal numbers, Journal of Integer Sequences, 27(5), 2024.

Crossrefs

Cf. A005153, A051624.