A373616 Positive integers that cannot be written as a sum of a practical number and a 13-gonal number.

10, 11, 22, 23, 26, 27, 34, 35, 39, 46, 47, 50, 51, 58, 59, 62, 63, 70, 75, 83, 87, 95, 99, 107, 111, 115, 122, 137, 138, 146, 149, 152, 159, 165, 167, 184, 185, 188, 194, 206, 218, 222, 245, 248, 263, 282, 284, 287, 314, 329, 345, 354, 357, 359, 362, 383, 386

Offset: 1

Author

Duc Van Khanh Tran, Jun 11 2024

Keywords

• nonn
• hard

Comments

Somu and Tran (2024) conjectured that there are finitely many such integers. It was also conjectured that 1612172 is the largest such integer. This conjecture was checked up to 10^8.

Examples

			11 is in the sequence as 13-gonal numbers below 11 are 0, 1 and both 11-0 and 11-1 are not practical. - _David A. Corneth_, Jun 11 2024
		

Links

• Duc Van Khanh Tran, Table of n, a(n) for n = 1..609
• 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, A051865.